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2017 A generalization of Kato's local $\varepsilon$-conjecture for $(\varphi,\Gamma)$-modules over the Robba ring
Kentaro Nakamura
Algebra Number Theory 11(2): 319-404 (2017). 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.

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Kentaro Nakamura. "A generalization of Kato's local $\varepsilon$-conjecture for $(\varphi,\Gamma)$-modules over the Robba ring." Algebra Number Theory 11 (2) 319 - 404, 2017. https://doi.org/10.2140/ant.2017.11.319

Information

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

zbMATH: 06722472
MathSciNet: MR3641877
Digital Object Identifier: 10.2140/ant.2017.11.319

Subjects:
Primary: 11F80
Secondary: 11F85, 11S25

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2017
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