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Number Theory Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2012/12/19
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Kentarou Nakamura (Hokkaido University)
A generalization of Kato's local epsilon conjecture for
(φ, Γ)-modules over the Robba ring (JAPANESE)
Kentarou Nakamura (Hokkaido University)
A generalization of Kato's local epsilon conjecture for
(φ, Γ)-modules over the Robba ring (JAPANESE)
[ Abstract ]
In his preprint “Lectures on the approach to Iwasawa theory of Hasse-Weil L-functions via B_dR, Part II ", Kazuya Kato proposed a conjecture called local epsilon conjecture. This conjecture predicts that the determinant of the Galois cohomology of a family of p-adic Galois representations has a canonical base whose specializations at de Rham points can be characterized by using Bloch-Kato exponential, L-factors and Deligne-Langlands epsilon constants of the associated Weil-Deligne representations.
In my talk, I generalize his conjecture for families of (φ, Γ)-modules over the Robba ring, and prove a part of this conjecture in the trianguline case. The two key ingredients are the recent result of Kedlaya-Pottharst-Xiao on the finiteness of cohomologies of (φ, Γ)-modules and my result on Bloch-Kato exponential map for (φ, Γ)-modules.
In his preprint “Lectures on the approach to Iwasawa theory of Hasse-Weil L-functions via B_dR, Part II ", Kazuya Kato proposed a conjecture called local epsilon conjecture. This conjecture predicts that the determinant of the Galois cohomology of a family of p-adic Galois representations has a canonical base whose specializations at de Rham points can be characterized by using Bloch-Kato exponential, L-factors and Deligne-Langlands epsilon constants of the associated Weil-Deligne representations.
In my talk, I generalize his conjecture for families of (φ, Γ)-modules over the Robba ring, and prove a part of this conjecture in the trianguline case. The two key ingredients are the recent result of Kedlaya-Pottharst-Xiao on the finiteness of cohomologies of (φ, Γ)-modules and my result on Bloch-Kato exponential map for (φ, Γ)-modules.
