Sur un problème de compatibilité local-global localement analytique

IF 2 4区数学 Q1 MATHEMATICS

Memoirs of the American Mathematical Society Pub Date : 2023-10-01 DOI:10.1090/memo/1442

Christophe Breuil, Yiwen Ding

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Puis on démontre plusieurs cas particuliers ou partiels de cette conjecture “améliorée”, notamment pour <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G upper L 3 left-parenthesis double-struck upper Q Subscript p Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>GL</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">\\operatorname {GL}_3(\\mathbb {Q}_{p})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Abstract. 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Then we prove several special or partial cases of this “improved” conjecture, notably for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G upper L 3 left-parenthesis double-struck upper Q Subscript p Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>GL</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">\\operatorname {GL}_3(\\mathbb {Q}_{p})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"121 1","pages":"0"},"PeriodicalIF":2.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Memoirs of the American Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/memo/1442","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

On réinterprète et on précise la conjecture du E x t 1 Ext^1 localement analytique de \cite{Br1} de manière fonctorielle en utilisant les ( φ , Γ ) (\varphi ,\Gamma ) -modules sur l’anneau de Robba (avec éventuellement de la t t -torsion). Puis on démontre plusieurs cas particuliers ou partiels de cette conjecture “améliorée”, notamment pour GL 3 ⁡ ( Q p ) \operatorname {GL}_3(\mathbb {Q}_{p}) . Abstract. We reinterpret the main conjecture of \cite{Br1} on the locally analytic E x t 1 Ext^1 in a functorial way using ( φ , Γ ) (\varphi ,\Gamma ) -modules (possibly with t t -torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this “improved” conjecture, notably for GL 3 ⁡ ( Q p ) \operatorname {GL}_3(\mathbb {Q}_{p}) .

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局部-全局兼容性问题局部分析

我们全球而且准确的猜想E x t Ext ^ 1 \引述分析当地Br1} fonctorielle地使用(φ,Γ\ \ varphi,环比上-modules 23% (Gamma)可能与-torsion t t)。然后几个特例证明这个猜想或局部的“改善”,特别是为GL 3⁡GL (p) Q \ operatorname {} _3 _ (Q \ mathbb {} {} p)。文摘。(We the hand of \猜想reinterpret引用Br1} on the locally analytic E x (t - Ext ^ 1 in a functorial使用(φΓway) (\ \ varphi、-modules (Gamma)也许,with -torsion t t) over the ring, 23%的making it more准确。几种prove Then we of this special黄金偏方格“改良”猜想,GL notably for 3⁡GL (p) Q \ operatorname {} _3 _ (Q \ mathbb {} {} p)。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.