A generalization of Kato’s local 𝜀-conjecture for (φ,Γ)-modules over the Robba ring

Nakamura, Kentaro

doi:10.2140/ant.2017.11.319

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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

DOI: 10.2140/ant.2017.11.319

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

Vol. 11, No. 2, 2017