Breuil-Mézard conjectures for central division algebras

2018/08/21 by Dotto, Andrea
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1808.06851

Abstract

We formulate an analogue of the Breuil-Mézard conjecture for the group of units of a central division algebra over a p-adic local field, and we prove that it follows from the conjecture for GL_n. To do so we construct a transfer of inertial types and Serre weights between the maximal compact subgroups of these two groups, in terms of Deligne-Lusztig theory, and we prove its compatibility with mod p reduction, via the inertial Jacquet-Langlands correspondence and certain explicit character formulas. We also prove analogous statements for ℓ-adic coefficients.

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