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Sur un problème de compatibilité local-global localement analytique
About this Title
Christophe Breuil and Yiwen Ding
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 290, Number 1442
ISBNs: 978-1-4704-6547-6 (print); 978-1-4704-7628-1 (online)
DOI: https://doi.org/10.1090/memo/1442
Published electronically: October 10, 2023
Keywords: Représentation localement analytique,
$(\varphi ,\Gamma$)-module généralisé,
compatibilité local-global
Table of Contents
Chapters
- 1. Introduction
- 2. Foncteurs $F_\alpha$ et $(\varphi ,\Gamma )$-modules sur l’anneau de Robba
- 3. Foncteurs $F_\alpha$ et théorie d’Orlik-Strauch
- 4. Quelques résultats d’exactitude pour $F_\alpha$
- 5. Foncteurs $F_\alpha$, groupes Ext${}^1$ et compatibilité local-global
- A. Appendice
Abstract
On réinterprète et on précise la conjecture du $Ext^1$ localement analytique de \cite{Br1} de manière fonctorielle en utilisant les $(\varphi ,\Gamma )$-modules sur l’anneau de Robba (avec éventuellement de la $t$-torsion). Puis on démontre plusieurs cas particuliers ou partiels de cette conjecture “améliorée”, notamment pour $\operatorname {GL}_3(\mathbb {Q}_{p})$.
Abstract. We reinterpret the main conjecture of \cite{Br1} on the locally analytic $Ext^1$ in a functorial way using $(\varphi ,\Gamma )$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this “improved” conjecture, notably for $\operatorname {GL}_3(\mathbb {Q}_{p})$.
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