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