A generalization of Kato's local epsilon-conjecture for (phi, Gamma)-modules over the Robba ring

作者：Nakamura Kentaro^*

来源：Algebra and Number Theory, 2017, 11(2): 319-404.

DOI：10.2140/ant.2017.11.319

• p-adic Hodge theory
• (phi, Gamma)-module
• B-pair

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

• 出版日期2017