2012/09/04 by David J. Hansen, David Hansen, Hansen, David · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1209.0710
41 pages, with an appendix by James Newton; Theorem 1.6 significantly improved; comments and corrections welcome
openalex publication_date 2012/09/04 · arxiv created 2012/10/01 · arxiv updated 2012/10/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We prove a universal coefficients theorem for the overconvergent cohomology modules introduced by Ash and Stevens, and give several applications. In particular, we sketch a very simple construction of eigenvarieties using overconvergent cohomology and prove many instances of a conjecture of Urban on the dimensions of these spaces. For example, when the underlying reductive group is an inner form of GL(2) over a quadratic imaginary extension of the rationals, the cuspidal component of the eigenvariety is a rigid analytic curve.