Proceedings of the American Mathematical Society最新文献

{"title":"Symplectic rigidity of O’Grady’s tenfolds","authors":"Luca Giovenzana, Annalisa Grossi, Claudio Onorati, Davide Veniani","doi":"10.1090/proc/16810","DOIUrl":"https://doi.org/10.1090/proc/16810","url":null,"abstract":"<p>We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O’Grady’s <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"10\"> <mml:semantics> <mml:mn>10</mml:mn> <mml:annotation encoding=\"application/x-tex\">10</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional deformation type is trivial.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of nuclear operators on spaces of vector-valued continuous functions with the strict topology","authors":"Juliusz Stochmal","doi":"10.1090/proc/16805","DOIUrl":"https://doi.org/10.1090/proc/16805","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be a completely regular Hausdorff space, let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;E&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;F&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; denote Banach spaces. Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Subscript b Baseline left-parenthesis upper X comma upper E right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;E&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;C_b(X,E)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; denote the space of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;E&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-valued bounded continuous functions on &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"beta\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;β&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;beta&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be the strict topology on this space. We establish the relationship between nuclear operators &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T colon upper C Subscript b Baseline left-parenthesis upper X comma upper E right-parenthesis right-arrow upper F\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo stretchy=\"false\"&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;T:C_b(X,E)rightar","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BMO-type functionals, total variation, and Γ-convergence","authors":"Panu Lahti, Quoc-Hung Nguyen","doi":"10.1090/proc/16812","DOIUrl":"https://doi.org/10.1090/proc/16812","url":null,"abstract":"&lt;p&gt;We study the BMO-type functional &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"kappa Subscript epsilon Baseline left-parenthesis f comma double-struck upper R Superscript n Baseline right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;κ&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;ε&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;f&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;kappa _{varepsilon }(f,mathbb {R}^n)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, which can be used to characterize bounded variation functions &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f element-of normal upper B normal upper V left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;f&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;B&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"normal\"&gt;V&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;fin mathrm {BV}(mathbb {R}^n)&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=\"normal upper Gamma\"&gt; &lt;mml:semantics&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Γ&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Gamma&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-limit of this functional, taken with respect to &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript normal l normal o normal c Superscript 1\"&gt; &lt;mml:semantics&gt; &lt;mml:msubsup&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;l&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"normal\"&gt;o&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"normal\"&gt;c&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msubsup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;L^1_{mathrm {loc}}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-convergence, is known to be &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"one fourth StartAbsoluteValue upper D f EndAbsoluteValue left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"&gt; &lt;mml:mfrac&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mn&gt;4&lt;/mml:mn&gt; &lt;/mml:mfrac&gt; &lt;/mml:mstyle&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;D&lt;/mml:mi&gt; &lt;mml:mi&gt;f&lt;/mml:mi&gt; &lt;mml:mro","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"32 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hodge numbers of desingularized fiber products of elliptic surfaces","authors":"Chad Schoen","doi":"10.1090/proc/16803","DOIUrl":"https://doi.org/10.1090/proc/16803","url":null,"abstract":"&lt;p&gt;Each element of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis double-struck upper Z Subscript greater-than-or-equal-to 0 Baseline right-parenthesis squared\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;Z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;≥&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;(Bbb Z_{geq 0})^2&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; is realized as the &lt;italic&gt;Hodge vector&lt;/italic&gt; &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis h Superscript 3 comma 0 Baseline left-parenthesis upper Z right-parenthesis comma h Superscript 2 comma 1 Baseline left-parenthesis upper Z right-parenthesis right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;h&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;3&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;Z&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;h&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;Z&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;(h^{3,0}(Z),h^{2,1}(Z))&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; of some compact, connected, three dimensional, complex, submanifold, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z subset-of double-struck upper P Subscript double-struck upper C Superscript upper N\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;Z&lt;/mml:mi&gt; &lt;mml:mo&gt;⊂&lt;/mml:mo&gt; &lt;mml:msubsup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;N&lt;/mml:mi&gt; &lt;/mml:msubsup&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Zsubset Bbb P^N_{Bbb C}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Each &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis x comma y right-parenthesis element-of left-parenthesis double-struck upper Z Subscript greater-than-or-equal-to 1 Baseline right-parenthesis squared\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;y&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;Z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt;","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"32 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the realisation problem for mapping degree sets","authors":"Christoforos Neofytidis, Hongbin Sun, Ye Tian, Shicheng Wang, Zhongzi Wang","doi":"10.1090/proc/16712","DOIUrl":"https://doi.org/10.1090/proc/16712","url":null,"abstract":"","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"38 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equality between the Bergman metric and Carathéodory metric","authors":"Bo-Yong Chen, Yuanpu Xiong, Liyou Zhang","doi":"10.1090/proc/16799","DOIUrl":"https://doi.org/10.1090/proc/16799","url":null,"abstract":"<p>We present an equality between the Bergman metric and Carathéodry metric.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dihedral Artin representations and CM fields","authors":"David Rohrlich","doi":"10.1090/proc/16793","DOIUrl":"https://doi.org/10.1090/proc/16793","url":null,"abstract":"<p>For a fixed CM 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> with maximal totally real subfield <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we consider isomorphism classes of dihedral Artin representations of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are induced from <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>, distinguishing between those which are “canonically” induced from <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> and those which are “noncanonically” induced from <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>. The latter can arise only for Artin representations with image isomorphic to the dihedral group of order 8. We show that asymptotically, the number of noncanonically induced isomorphism classes is always comparable to and in some cases exceeds the number of canonically induced ones.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on rearrangement Poincaré inequalities and the doubling condition","authors":"Joaquim Martín, Walter A. Ortiz","doi":"10.1090/proc/16795","DOIUrl":"https://doi.org/10.1090/proc/16795","url":null,"abstract":"<p>We introduce Poincaré-type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"63 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Every Δ⁰₂ Polish space is computable topological","authors":"Nikolay Bazhenov, Alexander Melnikov, Keng Meng Ng","doi":"10.1090/proc/16797","DOIUrl":"https://doi.org/10.1090/proc/16797","url":null,"abstract":"<p>We show that every <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Delta 2 Superscript 0\"> <mml:semantics> <mml:msubsup> <mml:mi mathvariant=\"normal\">Δ</mml:mi> <mml:mn>2</mml:mn> <mml:mn>0</mml:mn> </mml:msubsup> <mml:annotation encoding=\"application/x-tex\">Delta ^0_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Polish space admits a computable topological presentation given by an effective indexing of some non-empty open sets in the space.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Negative eigenvalues of the conformal Laplacian","authors":"Guillermo Henry, Jimmy Petean","doi":"10.1090/proc/16798","DOIUrl":"https://doi.org/10.1090/proc/16798","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be a closed differentiable manifold of dimension at least &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"&gt; &lt;mml:semantics&gt; &lt;mml:mn&gt;3&lt;/mml:mn&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;3&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Lamda 0 left-parenthesis upper M right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Λ&lt;/mml:mi&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;M&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;Lambda _0 (M)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be the minimum number of non-positive eigenvalues that the conformal Laplacian of a metric on &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; can have. We prove that for any &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"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; greater than or equal to &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Lamda 0 left-parenthesis upper M right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi mathvariant=\"normal\"&gt;Λ&lt;/mml:mi&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;M&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;Lambda _0 (M)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, there exists a Riemannian metric on &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; such that its conformal Laplacian has exactly &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"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; negative eigenvalues. Also, we discuss upper bounds for &lt;inline-formula content-type=\"math/mathm","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"33 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}