A derived construction of eigenvarieties

2021/10/10 by Weibo Fu, Fu, Weibo
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.04797

openalex publication_date 2021/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of p-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes associated to the locally symmetric spaces of a quasi-split reductive group \mathbbG, comparison to overconvergent cohomology, proving exactness of finite slope part functor, together with some representation-theoretic statements. As a global application, we exhibit an eigenvariety coming from data of GL_n over a CM field as a subeigenvariety for a quasi-split unitary group.

Related

• Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
• Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties
• S-arithmetic (co)homology and p-adic automorphic forms
• Universal coefficients for overconvergent cohomology and the geometry of eigenvarieties
• Resolutions for Locally Analytic Representations