Multiplicity one at full congruence level
| Autor: | Daniel Le, Benjamin Schraen, Stefano Morra |
|---|---|
| Přispěvatelé: | Department of Mathematics [University of Toronto], University of Toronto, Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Centre de Mathématiques Laurent Schwartz (CMLS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics - Number Theory General Mathematics Mathematics::Number Theory 010102 general mathematics Multiplicity (mathematics) 01 natural sciences Cohomology [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 010307 mathematical physics 0101 mathematics Mathematics::Representation Theory Mathematics Vector space Real field |
| Zdroj: | Journal of the Institute of Mathematics of Jussieu Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), In press, ⟨10.1017/S1474748020000225⟩ |
| ISSN: | 1474-7480 1475-3030 |
| DOI: | 10.1017/S1474748020000225⟩ |
| Popis: | Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular Galois representation which satisfies the Taylor--Wiles hypotheses and is tamely ramified and generic at a place $v$ above $p$. Let $\mathfrak{m}$ be the corresponding Hecke eigensystem. We describe the $\mathfrak{m}$-torsion in the mod $p$ cohomology of Shimura curves with full congruence level at $v$ as a $\mathrm{GL}_2(k_v)$-representation. In particular, it only depends on $\overline{r}|_{I_{F_v}}$ and its Jordan--H\"{o}lder factors appear with multiplicity one. The main ingredients are a description of the submodule structure for generic $\mathrm{GL}_2(\mathbb{F}_q)$-projective envelopes and the multiplicity one results of \cite{EGS}. Comment: Accepted for publication at Journal de l Institut de Mathematiques de Jussieu |
| Databáze: | OpenAIRE |
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