Ramification bounds via Wach modules and q‐crystalline cohomology
Abstract
Abstract Let be an absolutely unramified ‐adic field. We establish a ramification bound, depending only on the given prime and an integer , for mod Galois representations associated with Wach modules of height at most . Using an instance of ‐crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of for a smooth proper ‐adic formal scheme over , for arbitrarily large degree .
Fields of Study & Subjects
Algebraic structures and combinatorial models
Rings
Modules
and Algebras
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN