Asymptotic values of modular multiplicities for GL2
Abstract
We study the irreducible constituents of the reduction modulo p of irreducible algebraic representations V of ResK/Qp GL2 for K a finite extension of Qp. 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-M\'ezard conjecture.
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