Une interpr\'etation modulaire de la vari\'et\'e trianguline
| Autor: | Eugen Hellmann, Benjamin Schraen, Christophe Breuil |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-11-BS01-0005,ThéHopaD,Théorie de Hodge p-adique et développements(2011) |
| Jazyk: | francouzština |
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Modularity (networks) Conjecture Mathematics - Number Theory General Mathematics Mathematics::Number Theory 010102 general mathematics Local ring MSC 11F85 22E50 Galois module Space (mathematics) 01 natural sciences Cohomology Combinatorics 0103 physical sciences FOS: Mathematics 11F85 22E50 010307 mathematical physics Number Theory (math.NT) 0101 mathematics Representation Theory (math.RT) [MATH]Mathematics [math] Mathematics - Representation Theory Mathematics |
| Zdroj: | Mathematische Annalen Mathematische Annalen, Springer Verlag, 2016, 367 (3-4), pp.1587--1645. ⟨10.1007/s00208-016-1422-1⟩ |
| ISSN: | 0025-5831 1432-1807 |
| DOI: | 10.1007/s00208-016-1422-1⟩ |
| Popis: | Using a patching module constructed in recent work of Caraiani, Emerton, Gee, Geraghty, Pa{\v{s}}k{\=u}nas and Shin we construct some kind of analogue of an eigenvariety. We can show that this patched eigenvariety agrees with a union of irreducible components of a space of trianguline Galois representations. Building on this we discuss the relation with the modularity conjectures for the crystalline case, a conjecture of Breuil on the locally analytic socle of representations occurring in completed cohomology and with a conjecture of Bella\"iche and Chenevier on the complete local ring at certain points of eigenvarieties. Comment: in French |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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