S-arithmetic (co)homology and p-adic automorphic forms

2022/07/10 by Guillem Tarrach, Tarrach, Guillem
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2207.04554

openalex publication_date 2022/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the S-arithmetic (co)homology of reductive groups over number fields with coefficients in (duals of) certain locally algebraic and locally analytic representations for finite sets of primes S. We use our results to construct eigenvarieties associated to parabolic subgroups at places in S and certain classes of supercuspidal and algebraic representations of their Levi factors. We show that these agree with eigenvarieties constructed using overconvergent homology and that for definite unitary groups they are closely related to the Bernstein eigenvarieties constructed by Breuil-Ding.

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