Journal of the American Mathematical Society最新文献

{"title":"Part 1 of Martin’s Conjecture for order-preserving and measure-preserving functions","authors":"Patrick Lutz, Benjamin Siskind","doi":"10.1090/jams/1046","DOIUrl":"https://doi.org/10.1090/jams/1046","url":null,"abstract":"<p>Martin’s Conjecture is a proposed classification of the definable functions on the Turing degrees. It is usually divided into two parts, the first of which classifies functions which are <italic>not</italic> above the identity and the second of which classifies functions which are above the identity. Slaman and Steel proved the second part of the conjecture for Borel functions which are order-preserving (i.e. which preserve Turing reducibility). We prove the first part of the conjecture for all order-preserving functions. We do this by introducing a class of functions on the Turing degrees which we call “measure-preserving” and proving that part 1 of Martin’s Conjecture holds for all measure-preserving functions and also that all nontrivial order-preserving functions are measure-preserving. Our result on measure-preserving functions has several other consequences for Martin’s Conjecture, including an equivalence between part 1 of the conjecture and a statement about the structure of the Rudin-Keisler order on ultrafilters on the Turing degrees.</p>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"186 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algebraic cobordism and a Conner–Floyd isomorphism for algebraic K-theory","authors":"Toni Annala, Marc Hoyois, Ryomei Iwasa","doi":"10.1090/jams/1045","DOIUrl":"https://doi.org/10.1090/jams/1045","url":null,"abstract":"&lt;p&gt;We formulate and prove a Conner–Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal infinity\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∞&lt;!-- ∞ --&gt;&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;infty&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-category of non-&lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper A Superscript 1\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;A&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {A}^1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-invariant motivic spectra, which turns out to be equivalent to the &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal infinity\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∞&lt;!-- ∞ --&gt;&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;infty&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-category of fundamental motivic spectra satisfying elementary blowup excision, previously introduced by the first and third authors. We prove that this &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal infinity\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;∞&lt;!-- ∞ --&gt;&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;infty&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-category satisfies &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 1\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-homotopy invariance and weighted &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper A Superscript 1\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;A&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {A}^1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-homotopy invariance, which we use in place of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper A Superscript 1\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;A&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {A}^1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-ho","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"10 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Purity in chromatically localized algebraic 𝐾-theory","authors":"Markus Land, Akhil Mathew, Lennart Meier, Georg Tamme","doi":"10.1090/jams/1043","DOIUrl":"https://doi.org/10.1090/jams/1043","url":null,"abstract":"&lt;p&gt;We prove a purity property in telescopically localized algebraic &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-theory of ring spectra: For &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than-or-equal-to 1\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;≥&lt;!-- ≥ --&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;ngeq 1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, the &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T left-parenthesis n right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;T(n)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-localization of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-parenthesis upper R right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;R&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;K(R)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; only depends on the &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T left-parenthesis 0 right-parenthesis circled-plus midline-horizontal-ellipsis circled-plus upper T left-parenthesis n right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;⊕&lt;!-- ⊕ --&gt;&lt;/mml:mo&gt; &lt;mml:mo&gt;⋯&lt;!-- ⋯ --&gt;&lt;/mml:mo&gt; &lt;mml:mo&gt;⊕&lt;!-- ⊕ --&gt;&lt;/mml:mo&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;T(0)oplus dots oplus T(n)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-localization of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;R&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;R&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. This complements a classical result of Waldhausen in rational &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-theory. Combining our result with work o","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"246 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The singular set in the Stefan problem","authors":"Alessio Figalli, Xavier Ros-Oton, Joaquim Serra","doi":"10.1090/jams/1026","DOIUrl":"https://doi.org/10.1090/jams/1026","url":null,"abstract":"","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The singularity probability of a random symmetric matrix is exponentially small","authors":"Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe","doi":"10.1090/jams/1042","DOIUrl":"https://doi.org/10.1090/jams/1042","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be drawn uniformly at random from the set of all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> symmetric matrices with entries in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartSet negative 1 comma 1 EndSet\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{-1,1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that <disp-formula content-type=\"math/mathml\"> [ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P left-parenthesis det left-parenthesis upper A right-parenthesis equals 0 right-parenthesis less-than-or-slanted-equals e Superscript minus c n Baseline comma\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mo movablelimits=\"true\" form=\"prefix\">det</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mi>c</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {P}( det (A) = 0 ) leqslant e^{-cn},</mml:annotation> </mml:semantics> </mml:math> ] </disp-formula> where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"c greater-than 0\"> <mml:semantics> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">c&gt;0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an absolute constant, thereby resolving a long-standing conjecture.</p>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"No infinite spin for planar total collision","authors":"Richard Moeckel, Richard Montgomery","doi":"10.1090/jams/1044","DOIUrl":"https://doi.org/10.1090/jams/1044","url":null,"abstract":"<p>The infinite spin problem is an old problem concerning the rotational behavior of total collision orbits in the <italic>n</italic>-body problem. It has long been known that when a solution tends to total collision then its normalized configuration curve must converge to the set of normalized central configurations. In the planar n-body problem every normalized configuration determines a circle of rotationally equivalent normalized configurations and, in particular, there are circles of normalized central configurations. It’s conceivable that by means of an <italic>infinite spin</italic>, a total collision solution could converge to such a circle instead of to a particular point on it. Here we prove that this is not possible, at least if the limiting circle of central configurations is isolated from other circles of central configurations. (It is believed that all central configurations are isolated, but this is not known in general.) Our proof relies on combining the center manifold theorem with the Łojasiewicz gradient inequality.</p>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"38 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric local systems on very general curves and isomonodromy","authors":"Aaron Landesman, Daniel Litt","doi":"10.1090/jams/1038","DOIUrl":"https://doi.org/10.1090/jams/1038","url":null,"abstract":"We show that the minimum rank of a non-isotrivial local system of geometric origin on a suitably general <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pointed curve of genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is at least <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 StartRoot g plus 1 EndRoot\"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mi>g</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:msqrt> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">2sqrt {g+1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We apply this result to resolve conjectures of Esnault-Kerz and Budur-Wang. The main input is an analysis of stability properties of flat vector bundles under isomonodromic deformations, which additionally answers questions of Biswas, Heu, and Hurtubise.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"179 S446","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sectorial descent for wrapped Fukaya categories","authors":"Sheel Ganatra, John Pardon, Vivek Shende","doi":"10.1090/jams/1035","DOIUrl":"https://doi.org/10.1090/jams/1035","url":null,"abstract":"We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect to so-called Weinstein sectorial coverings and (2) that the partially wrapped Fukaya category of a Weinstein manifold with respect to a mostly Legendrian stop is generated by the cocores of the critical handles and the linking disks to the stop. We also prove (3) a ‘stop removal equals localization’ result, and (4) that the Fukaya–Seidel category of a Lefschetz fibration with Liouville fiber is generated by the Lefschetz thimbles. These results are derived from three main ingredients, also of independent use: (5) a Künneth formula (6) an exact triangle in the Fukaya category associated to wrapping a Lagrangian through a Legendrian stop at infinity and (7) a geometric criterion for when a pushforward functor between wrapped Fukaya categories of Liouville sectors is fully faithful.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"16 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Restricted trichotomy in characteristic zero","authors":"Benjamin Castle","doi":"10.1090/jams/1037","DOIUrl":"https://doi.org/10.1090/jams/1037","url":null,"abstract":"We prove the characteristic zero case of Zilber’s Restricted Trichotomy Conjecture. That is, we show that if <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is any non-locally modular strongly minimal structure interpreted in an algebraically closed field <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of characteristic zero, then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> itself interprets <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; in particular, any non-1-based structure interpreted in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is mutually interpretable with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Notably, we treat both the ‘one-dimensional’ and ‘higher-dimensional’ cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135689171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A structure theory for stable codimension 1 integral varifolds with applications to area minimising hypersurfaces mod 𝑝","authors":"Paul Minter, Neshan Wickramasekera","doi":"10.1090/jams/1032","DOIUrl":"https://doi.org/10.1090/jams/1032","url":null,"abstract":"For any &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q element-of StartSet three halves comma 2 comma five halves comma 3 comma ellipsis EndSet\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;Q&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;!-- ∈ --&gt;&lt;/mml:mo&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;{&lt;/mml:mo&gt; &lt;mml:mfrac&gt; &lt;mml:mn&gt;3&lt;/mml:mn&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mfrac&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mfrac&gt; &lt;mml:mn&gt;5&lt;/mml:mn&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mfrac&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;3&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mo&gt;…&lt;!-- … --&gt;&lt;/mml:mo&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;}&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Qin {frac {3}{2},2,frac {5}{2},3,dotsc }&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, we establish a structure theory for the class &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper S Subscript upper Q\"&gt; &lt;mml:semantics&gt; &lt;mml:msub&gt; &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt; &lt;mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\"&gt;S&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;Q&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathcal {S}_Q&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; of stable codimension 1 stationary integral varifolds admitting no classical singularities of density &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"greater-than upper Q\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mi&gt;Q&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;&gt;Q&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. This theory comprises three main theorems which describe the nature of a varifold &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V element-of script upper S Subscript upper Q\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;!-- ∈ --&gt;&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt; &lt;mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\"&gt;S&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;Q&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Vin mathcal {S}_Q&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; when: (i) &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;V&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; is close to a flat disk of multiplicity &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;Q&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Q&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; (for integer &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;m","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}