Asymptotic values of modular multiplicities for GL 2
Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 465-482.

We study the irreducible constituents of the reduction modulo p of irreducible algebraic representations V of the group Res K/ p GL 2 for K a finite extension of 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.

Valeurs asymptotiques de multiplicités modulaires pour GL 2 .

Nous étudions les constituants irréductibles de la réduction modulo p d’une représentation algébrique irréductible V du groupe Res K/ p GL 2 pour une extension finie K de p . Nous montrons qu’asymptotiquement, la multiplicité de chaque constituant ne dépend que de la dimension de V et du caractère central de sa réduction modulo p. Nous appliquons ce résultat au calcul de la valeur asymptotique de multiplicités qui sont l’objet de la conjecture de Breuil-Mézard.

DOI: 10.5802/jtnb.875
Sandra Rozensztajn 1

1 UMPA, ENS de Lyon UMR 5669 du CNRS 46, allée d’Italie 69364 Lyon Cedex 07 France
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Sandra Rozensztajn. Asymptotic values of modular multiplicities for $\operatorname{GL}_2$. Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 465-482. doi : 10.5802/jtnb.875. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.875/

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