Asymptotic values of modular multiplicities for GL 2

Sandra Rozensztajn[1]

  • [1] UMPA, ENS de Lyon UMR 5669 du CNRS 46, allée d’Italie 69364 Lyon Cedex 07 France

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 2, page 465-482
  • ISSN: 1246-7405

Abstract

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We study the irreducible constituents of the reduction modulo p of irreducible algebraic representations V of the group Res K / ℚ p GL 2 for K a finite extension of ℚ p . We show that asymptotically, the multiplicity of each constituent depends only on the dimension of V and the central character of its reduction modulo p . As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.

How to cite

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Rozensztajn, Sandra. "Asymptotic values of modular multiplicities for $\operatorname{GL}_2$." Journal de Théorie des Nombres de Bordeaux 26.2 (2014): 465-482. <http://eudml.org/doc/275787>.

@article{Rozensztajn2014,
abstract = {We study the irreducible constituents of the reduction modulo $p$ of irreducible algebraic representations $V$ of the group $\operatorname\{Res\}_\{K/\mathbb\{Q\}_p\}\operatorname\{GL\}_2$ for $K$ a finite extension of $\mathbb\{Q\}_p$. We show that asymptotically, the multiplicity of each constituent depends only on the dimension of $V$ and the central character of its reduction modulo $p$. As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.},
affiliation = {UMPA, ENS de Lyon UMR 5669 du CNRS 46, allée d’Italie 69364 Lyon Cedex 07 France},
author = {Rozensztajn, Sandra},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {10},
number = {2},
pages = {465-482},
publisher = {Société Arithmétique de Bordeaux},
title = {Asymptotic values of modular multiplicities for $\operatorname\{GL\}_2$},
url = {http://eudml.org/doc/275787},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Rozensztajn, Sandra
TI - Asymptotic values of modular multiplicities for $\operatorname{GL}_2$
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/10//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 2
SP - 465
EP - 482
AB - We study the irreducible constituents of the reduction modulo $p$ of irreducible algebraic representations $V$ of the group $\operatorname{Res}_{K/\mathbb{Q}_p}\operatorname{GL}_2$ for $K$ a finite extension of $\mathbb{Q}_p$. We show that asymptotically, the multiplicity of each constituent depends only on the dimension of $V$ and the central character of its reduction modulo $p$. As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.
LA - eng
UR - http://eudml.org/doc/275787
ER -

References

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