Galois cohomology of p-adic fields and (φ, τ)-modules

2022/01/26 by Zhao, Luming
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.11235

Abstract

We construct various explicit Herr complexes that compute the Galois cohomology of a p-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic 0 with a perfect residue field of characteristic p, using the associated (φ,τ)-modules (defined by Xavier Caruso), instead of (φ,Γ)-modules. We also give an application to p-divisible groups.

Related

• Galois cohomology of a p-adic field via (Φ,Γ)-modules in the imperfect residue field case
• The p-adic Galois Cohomology of Valuation Fields
• Cohomology and overconvergence for representations of powers of Galois\n groups
• Families of Galois representations and (φ, τ)-modules
• Locally analytic vectors and overconvergent (φ, τ)-modules