Modularity of trianguline Galois representations

Bellovin, R. (2024) Modularity of trianguline Galois representations. Forum of Mathematics, Sigma, 12, e3. (doi: 10.1017/fms.2023.116)

Abstract

We use the theory of trianguline (φ, Γ)-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients. The use of pseudorigid spaces lets us construct integral models of the trianguline varieties of [BHS17], [Che13] after bounding the slope, and we carry out a Taylor–Wiles patching argument for families of overconvergent modular forms. This permits us to construct a patched quaternionic eigenvariety and deduce our modularity results.

• 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: Forum of Mathematics, Sigma
• Publisher: Cambridge University Press
• ISSN: 2050-5094
• ISSN (Online): 2050-5094
• Published Online: 05 January 2024
• Copyright Holders: Copyright © 2024 The Author
• First Published: First published in Forum of Mathematics, Sigma 12: e3
• Publisher Policy: Reproduced under a Creative Commons License