Cohomology of (ϕ, Γ)-modules over pseudorigid spaces

Bellovin, R. (2024) Cohomology of (ϕ, Γ)-modules over pseudorigid spaces. International Mathematics Research Notices, 2024(4), pp. 2999-3051. (doi: 10.1093/imrn/rnad093)

Abstract

We study the cohomology of families of (ϕ, )-modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify rank-1 (ϕ, )-modules and deduce that triangulations of pseudorigid families of (ϕ, )-modules can be interpolated, extending a result of [29]. We then apply this to study extended eigenvarieties at the boundary of weight space, proving in particular that the eigencurve is proper at the boundary and that Galois representations attached to certain characteristic p points are trianguline.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellovin, Dr Rebecca
• Authors: Bellovin, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Published Online: 16 May 2023
• Copyright Holders: Copyright © The Author(s) 2023.
• First Published: First published in International Mathematics Research Notices 2024(4):2999–3051
• Publisher Policy: Reproduced under a Creative Commons license