Iwasawa theory of de Rham (ϕ,Γ)-modules over the Robba rings

2012/01/31 by Kentaro Nakamura, Nakamura, Kentaro
Arts and Humanities · Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1201.6475

openalex publication_date 2012/01/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The aim of this article is to study Bloch-Kato's exponential map and Perrin-Riou's "big" exponential map purely in terms of (ϕ,Γ)-modules over the Robba ring. We first generalize the definition of Bloch-Kato's exponential map for all the (ϕ,Γ)-modules without using Fontaine's rings B_cris, B_dR of p-adic periods and then we generalize the construction of Perrin-Riou's "big" exponential map for all the de Rham (ϕ,Γ)-modules and prove that this map interpolates our Bloch-Kato's exponential map and the dual exponential map. Finally, we prove a theorem concerning to the determinant of our "big" exponential map, which is a generalization of Perrin-Riou's δ(V)-conjecture. The key ingredients for our study are Pottharst's theory of analytic Iwasawa cohomology and Berger's construction of p-adic differential equations associated to de Rham (ϕ,Γ)-modules.

Citations

• Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations

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