Cohomology of (φ, τ)-modules

2024/02/04 by Gao, Hui, Zhao, Luming · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.02492

Abstract

We construct cohomology theories for (φ, τ)-modules, and study their relation with cohomology of (φ, Γ)-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the étale case, the overconvergent case, and the rigid-overconvergent case simultaneously. We use recent advances in locally analytic cohomology as a key ingredient.

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• Multivariable period rings of p-adic false Tate curve extension

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• Comparisons of Lie algebra cohomologies of (φ,Γ)-modules
• Finiteness and duality of cohomology of (φ,Γ)-modules and the 6-functor formalism of locally analytic representations
• Cohomology of arithmetic families of (phi,Gamma)-modules
• Invitation to higher local fields, Part II, section 6: Phi-Gamma-modules and Galois cohomology
• Galois cohomology of p-adic fields and (φ, τ)-modules