Comparisons of Lie algebra cohomologies of (φ,Γ)-modules

2023/11/13 by Rustam Steingart, Steingart, Rustam
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2311.07799

Abstract

We generalise a result of Fourquaux and Xie thereby completely determining the relationship between ℚ_p and L-analytic Lie algebra cohomology of analytic (φ_L,Γ_L)-modules. We use the results to conclude that for L≠ ℚ_p, there exist examples of étale (φ_L,Γ_L)-modules over Robba rings whose ℚ_p-analytic cohomology does not arise as a base change of Galois cohomology.

Related

• Cohomology of (φ, τ)-modules
• Finiteness and duality of cohomology of (φ,Γ)-modules and the 6-functor formalism of locally analytic representations
• (φ,Γ)-modules over relatively discrete algebras
• Relative p-adic Hodge theory: Foundations
• Galois Cohomology for Lubin-Tate (φ_q,Γ_LT)-modules over Coefficient rings