{"title":"局部-全局兼容性问题局部分析","authors":"Christophe Breuil, Yiwen Ding","doi":"10.1090/memo/1442","DOIUrl":null,"url":null,"abstract":"On réinterprète et on précise la conjecture du <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E x t Superscript 1\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Ext^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> localement analytique de \\cite{Br1} de manière fonctorielle en utilisant les <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis phi comma normal upper Gamma right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>φ<!-- φ --></mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=\"normal\">Γ<!-- Γ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(\\varphi ,\\Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules sur l’anneau de Robba (avec éventuellement de la <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding=\"application/x-tex\">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-torsion). 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. We reinterpret the main conjecture of \\cite{Br1} on the locally analytic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E x t Superscript 1\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Ext^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a functorial way using <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis phi comma normal upper Gamma right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>φ<!-- φ --></mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=\"normal\">Γ<!-- Γ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(\\varphi ,\\Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules (possibly with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding=\"application/x-tex\">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-torsion) over the Robba ring, making it more accurate. 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":"{\"title\":\"Sur un problème de compatibilité local-global localement analytique\",\"authors\":\"Christophe Breuil, Yiwen Ding\",\"doi\":\"10.1090/memo/1442\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"On réinterprète et on précise la conjecture du <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E x t Superscript 1\\\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">Ext^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> localement analytique de \\\\cite{Br1} de manière fonctorielle en utilisant les <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"left-parenthesis phi comma normal upper Gamma right-parenthesis\\\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>φ<!-- φ --></mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=\\\"normal\\\">Γ<!-- Γ --></mml:mi> <mml:mo stretchy=\\\"false\\\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">(\\\\varphi ,\\\\Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules sur l’anneau de Robba (avec éventuellement de la <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"t\\\"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-torsion). 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. We reinterpret the main conjecture of \\\\cite{Br1} on the locally analytic <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E x t Superscript 1\\\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">Ext^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a functorial way using <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"left-parenthesis phi comma normal upper Gamma right-parenthesis\\\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>φ<!-- φ --></mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=\\\"normal\\\">Γ<!-- Γ --></mml:mi> <mml:mo stretchy=\\\"false\\\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">(\\\\varphi ,\\\\Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules (possibly with <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"t\\\"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-torsion) over the Robba ring, making it more accurate. 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}","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
摘要
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 3GL (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 3GL (p) Q \ operatorname {} _3 _ (Q \ mathbb {} {} p)。
Sur un problème de compatibilité local-global localement analytique
On réinterprète et on précise la conjecture du Ext1Ext^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 tt-torsion). Puis on démontre plusieurs cas particuliers ou partiels de cette conjecture “améliorée”, notamment pour GL3(Qp)\operatorname {GL}_3(\mathbb {Q}_{p}). Abstract. We reinterpret the main conjecture of \cite{Br1} on the locally analytic Ext1Ext^1 in a functorial way using (φ,Γ)(\varphi ,\Gamma )-modules (possibly with tt-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this “improved” conjecture, notably for GL3(Qp)\operatorname {GL}_3(\mathbb {Q}_{p}).
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