Sur un problème de compatibilité local-global localement analytique

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials 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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/memo/1442","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464