Journal of the American Mathematical Society最新文献

{"title":"Zéro-cycles sur les espaces homogènes et problème de Galois inverse","authors":"Yonatan Harpaz, Olivier Wittenberg","doi":"10.1090/jams/943","DOIUrl":"https://doi.org/10.1090/jams/943","url":null,"abstract":"Let X be a smooth compactification of a homogeneous space of a linear algebraic group G over a number field k. We establish the conjecture of Colliot-Th'el`ene, Sansuc, Kato and Saito on the image of the Chow group of zero-cycles of X in the product of the same groups over all the completions of k. When G is semisimple and simply connected and the geometric stabiliser is finite and supersolvable, we show that rational points of X are dense in the Brauer-Manin set. For finite supersolvable groups, in particular for finite nilpotent groups, this yields a new proof of Shafarevich's theorem on the inverse Galois problem, and solves, at the same time, Grunwald's problem, for these groups. \u0000----- \u0000Soit X une compactification lisse d'un espace homog`ene d'un groupe alg'ebrique lin'eaire G sur un corps de nombres k. Nous 'etablissons la conjecture de Colliot-Th'el`ene, Sansuc, Kato et Saito sur l'image du groupe de Chow des z'ero-cycles de X dans le produit des m^emes groupes sur tous les compl'et'es de k. Lorsque G est semi-simple et simplement connexe et que le stabilisateur g'eom'etrique est fini et hyper-r'esoluble, nous montrons que les points rationnels de X sont denses dans l'ensemble de Brauer-Manin. Pour les groupes finis hyper-r'esolubles, en particulier pour les groupes finis nilpotents, cela donne une nouvelle preuve du th'eor`eme de Shafarevich sur le probl`eme de Galois inverse et r'esout en m^eme temps, pour ces groupes, le probl`eme de Grunwald.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/943","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42336799","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":"Examples of compact Einstein four-manifolds with negative curvature","authors":"J. Fine, Bruno Premoselli","doi":"10.1090/jams/944","DOIUrl":"https://doi.org/10.1090/jams/944","url":null,"abstract":"<p>We give new examples of compact, negatively curved Einstein manifolds of dimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4\">\u0000 <mml:semantics>\u0000 <mml:mn>4</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">4</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of four-manifolds <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper X Subscript k Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(X_k)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> previously considered by Gromov and Thurston (Pinching constants for hyperbolic manifolds, <italic>Invent. Math.</italic> <bold>89</bold> (1987), no. 1, 1–12). The construction begins with a certain sequence <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper M Subscript k Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(M_k)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of hyperbolic four-manifolds, each containing a totally geodesic surface <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma Subscript k\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi mathvariant=\"normal\">Σ<!-- Σ --></mml:mi>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">Sigma _k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> which is nullhomologous and whose normal injectivity radius tends to infinity with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. For a fixed choice of natural number <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"l\">\u0000 <mml:semantics>\u0000 <mml:mi>l</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">l</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, we consider the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/944","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48590677","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":"Weak functoriality of Cohen-Macaulay algebras","authors":"Y. Andre","doi":"10.1090/jams/937","DOIUrl":"https://doi.org/10.1090/jams/937","url":null,"abstract":"We prove the weak functoriality of (big) Cohen-Macaulay algebras, which controls the whole skein of “homological conjectures” in commutative algebra; namely, for any local homomorphism \u0000\u0000 \u0000 \u0000 R\u0000 →\u0000 \u0000 R\u0000 ′\u0000 \u0000 \u0000 Rto R’\u0000 \u0000\u0000 of complete local domains, there exists a compatible homomorphism between some Cohen-Macaulay \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000-algebra and some Cohen-Macaulay \u0000\u0000 \u0000 \u0000 R\u0000 ′\u0000 \u0000 R’\u0000 \u0000\u0000-algebra.\u0000\u0000When \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000 contains a field, this is already known. When \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000 is of mixed characteristic, our strategy of proof is reminiscent of G. Dietz’s refined treatment of weak functoriality of Cohen-Macaulay algebras in characteristic \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000; in fact, developing a “tilting argument” due to K. Shimomoto, we combine the perfectoid techniques of the author’s earlier work with Dietz’s result.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/937","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42450319","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":"Cluster theory of the coherent Satake category","authors":"Sabin Cautis, H. Williams","doi":"10.1090/JAMS/918","DOIUrl":"https://doi.org/10.1090/JAMS/918","url":null,"abstract":"<p>We study the category of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G left-parenthesis script upper O right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">G(mathcal {O})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-equivariant perverse coherent sheaves on the affine Grassmannian <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper G normal r Subscript upper G\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">G</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">r</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {Gr}_G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. This coherent Satake category is not semisimple and its convolution product is not symmetric, in contrast with the usual constructible Satake category. Instead, we use the Beilinson-Drinfeld Grassmannian to construct renormalized <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\">\u0000 <mml:semantics>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-matrices. These are canonical nonzero maps between convolution products which satisfy axioms weaker than those of a braiding.</p>\u0000\u0000<p>We also show that the coherent Satake category is rigid, and that together these results strongly constrain its convolution structure. In particular, they can be used to deduce the existence of (categorified) cluster structures. We study the case <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G equals upper G upper L Subscript n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">G = GL_n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in detail and prove that the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper G Subscript m\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>m</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {G}_m</","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAMS/918","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49643672","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 test function conjecture for parahoric local models","authors":"T. Haines, Timo Richarz","doi":"10.1090/jams/955","DOIUrl":"https://doi.org/10.1090/jams/955","url":null,"abstract":"We prove the test function conjecture of Kottwitz and the first-named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43784633","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":"Stably irrational hypersurfaces of small slopes","authors":"Stefan Schreieder","doi":"10.1090/jams/928","DOIUrl":"https://doi.org/10.1090/jams/928","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be an uncountable field of characteristic different from two. We show that a very general hypersurface <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X subset-of double-struck upper P Subscript k Superscript upper N plus 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">P</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Xsubset mathbb {P}^{N+1}_k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of dimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N greater-than-or-equal-to 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ngeq 3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and degree at least <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"log Subscript 2 Baseline upper N plus 2\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>log</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">log _2N +2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is not stably rational over the algebraic closure of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/928","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49661592","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":"On the constant scalar curvature Kähler metrics (II)—Existence results","authors":"Xiuxiong Chen, Jingrui Cheng","doi":"10.1090/jams/966","DOIUrl":"https://doi.org/10.1090/jams/966","url":null,"abstract":"&lt;p&gt;In this paper, we apply our previous estimates in Chen and Cheng [&lt;italic&gt;On the constant scalar curvature Kähler metrics (I): a priori estimates&lt;/italic&gt;, Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;K&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-energy in terms of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 1\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mi&gt;L&lt;/mml:mi&gt;\u0000 &lt;mml:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;L^1&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; geodesic distance &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d 1\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msub&gt;\u0000 &lt;mml:mi&gt;d&lt;/mml:mi&gt;\u0000 &lt;mml:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:msub&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;d_1&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; in the space of Kähler potentials implies the existence of cscK metrics. We also show that the weak minimizers of the &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;K&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-energy in &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis script upper E Superscript 1 Baseline comma d 1 right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\"&gt;E&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:mo&gt;,&lt;/mml:mo&gt;\u0000 &lt;mml:msub&gt;\u0000 &lt;mml:mi&gt;d&lt;/mml:mi&gt;\u0000 &lt;mml:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:msub&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;(mathcal {E}^1, d_1)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; are smooth cscK potentials. Finally we show that the non-existence of cscK metric implies the existence of a destabilized &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 1\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mi&gt;L&lt;/mml:mi&gt;\u0000 &lt;mml:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;L^1&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; geodesic ray where the &lt;inline-formula content-type=\"math/mathm","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47479415","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":"On the constant scalar curvature Kähler metrics (I)—A priori estimates","authors":"Xiuxiong Chen, Jingrui Cheng","doi":"10.1090/jams/967","DOIUrl":"https://doi.org/10.1090/jams/967","url":null,"abstract":"In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a \u0000\u0000 \u0000 \u0000 C\u0000 0\u0000 \u0000 C^0\u0000 \u0000\u0000 bound for the Kähler potential.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2017-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41965272","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":"Invariant metrics on negatively pinched complete Kähler manifolds","authors":"Damin Wu, S. Yau","doi":"10.1090/jams/933","DOIUrl":"https://doi.org/10.1090/jams/933","url":null,"abstract":"We prove that a complete Kähler manifold with holomorphic curvature bounded between two negative constants admits a unique complete Kähler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly equivalent to the background Kähler metric. Furthermore, all three metrics are shown to be uniformly equivalent to the Berg- man metric, if the complete Kähler manifold is simply-connected, with the sectional curvature bounded between two negative constants. In particular, we confirm two conjectures of R. E. Greene and H. Wu posted in 1979.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2017-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/933","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46913598","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":"Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic","authors":"A. Premet, David I. Stewart","doi":"10.1090/JAMS/926","DOIUrl":"https://doi.org/10.1090/JAMS/926","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;G&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;G&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be an exceptional simple algebraic group over an algebraically closed field &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;k&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;k&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; and suppose that &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p equals c h a r left-parenthesis k right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mi&gt;p&lt;/mml:mi&gt;\u0000 &lt;mml:mo&gt;=&lt;/mml:mo&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi&gt;char&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;k&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;p={operatorname {char}}(k)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is a good prime for &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;G&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;G&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;. In this paper we classify the maximal Lie subalgebras &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German m\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"fraktur\"&gt;m&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathfrak {m}&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; of the Lie algebra &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German g equals upper L i e left-parenthesis upper G right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"fraktur\"&gt;g&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mo&gt;=&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;Lie&lt;/mml:mi&gt;\u0000 &lt;mml:mo&gt;⁡&lt;!-- ⁡ --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;G&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathfrak {g}=operatorname {Lie}(G)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;. Specifically, we show that either &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German m equals upper L i e left-parenthesis upper M right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvarian","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2017-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAMS/926","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42391043","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}