2013/05/04 by Kentaro Nakamura, Nakamura, Kentaro
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1305.0880
74pages, 77pages(second version)
openalex publication_date 2013/05/04 · arxiv created 2015/02/15 · arxiv updated 2015/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this article is to generalize Kato's (commutative) p-adic local epsilon-conjecture [Ka93b] for families of (phi,Gamma)-modules over the Robba ring. In particular, we prove the generalized local epsilon-conjecture for rank one (phi,Gamma)-modules, which is a generalization of Kato's theorem [Ka93b] for rank one Galois representations. The key ingredients are the recent results of Kedlaya-Pottharst-Xiao [KPX12] on the finiteness of cohomology of (phi,Gamma)-modules and the theory of Bloch-Kato's exponential map for (phi,Gamma)-modules developed in [Na13].