Vol. 11, No. 2, 2017

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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

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.

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