Tamagawa numbers of some crystalline representations

2002/09/18 by Laurent Berger, Berger, Laurent
Mathematics · #11S #14F30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT #msc:11S #msc:14F30

paper · pdf · doi:10.48550/arxiv.math/0209233

12 pages, in French

arxiv created 2002/09/18 · openalex publication_date 2002/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to give a proof of the C_EP,F(V) conjecture for some semi-stable representations and of the δ_\Zp(V) conjecture for some crystalline representations. There are two major ingredients: first, the computation of Tamagawa numbers using a variation on results of Fontaine-Laffaille and of Bloch-Kato, and second some continuity results for Bloch-Kato's exponential which were proved by Perrin-Riou.

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