Finiteness and duality of cohomology of (φ,Γ)-modules and the 6-functor formalism of locally analytic representations

2025/04/02 by Yutaro Mikami, Mikami, Yutaro
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.01780

openalex publication_date 2025/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Finiteness and duality of cohomology of families of (φ,Γ)-modules were proved by Kedlaya-Pottharst-Xiao. In this paper, we study solid locally analytic representations introduced by Rodrigues Jacinto-Rodríguez Camargo in terms of analytic stacks and 6-functor formalisms, which are developed by Clausen-Scholze, Heyer-Mann, respectively. By using this, we provide a generalization of the result of Kedlaya-Pottharst-Xiao, giving a new proof for cases already proved there.

Related

• Cohomology of (φ, τ)-modules
• (φ,Γ)-modules over relatively discrete algebras
• Cohomology of arithmetic families of (phi,Gamma)-modules
• Associated primes of local cohomology modules
• Duality for admissible locally analytic representations