Vol. 11, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
A generalization of Kato's local $\varepsilon$-conjecture for $(\varphi,\Gamma)$-modules over the Robba ring

Kentaro Nakamura

Vol. 11 (2017), No. 2, 319–404
Abstract

We generalize Kato’s (commutative) p-adic local ε-conjecture for families of (φ,Γ)-modules over the Robba rings. In particular, we prove the essential parts of the generalized local ε-conjecture for families of trianguline (φ,Γ)-modules. The key ingredients are the author’s previous work on the Bloch–Kato exponential map for (φ,Γ)-modules and the recent results of Kedlaya, Pottharst and Xiao on the finiteness of cohomology of (φ,Γ)-modules.

Keywords
$p$-adic Hodge theory, $(\varphi,\Gamma)$-module, $B$-pair
Mathematical Subject Classification 2010
Primary: 11F80
Secondary: 11F85, 11S25
Milestones
Received: 8 August 2014
Revised: 11 October 2016
Accepted: 13 November 2016
Published: 15 April 2017
Authors
Kentaro Nakamura
Department of Mathematics
Saga University
1 Honjo-machi
Saga 840-8502
Japan