Algebra & Number Theory

A generalization of Kato's local $\varepsilon$-conjecture for $(\varphi,\Gamma)$-modules over the Robba ring

Kentaro Nakamura

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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.

Article information

Algebra Number Theory, Volume 11, Number 2 (2017), 319-404.

Received: 8 August 2014
Revised: 11 October 2016
Accepted: 13 November 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F80: Galois representations
Secondary: 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11S25: Galois cohomology [See also 12Gxx, 16H05]

$p$-adic Hodge theory $(\varphi,\Gamma)$-module $B$-pair


Nakamura, Kentaro. A generalization of Kato's local $\varepsilon$-conjecture for $(\varphi,\Gamma)$-modules over the Robba ring. Algebra Number Theory 11 (2017), no. 2, 319--404. doi:10.2140/ant.2017.11.319.

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