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Number Theory Seminar
Seminar information archive ～12/01｜Next seminar｜Future seminars 12/02～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
Next seminar
2025/12/03
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Takato Watanabe (University of Tokyo)
On p-adic Galois representations of monomial fields and p-adic differential modules on fake annuli
Takato Watanabe (University of Tokyo)
On p-adic Galois representations of monomial fields and p-adic differential modules on fake annuli
[ Abstract ]
The fake annuli introduced by Kedlaya are certain one-dimensional subannuli of p-adic polyannuli with multiple derivations. They are related to monomial fields, which are generalizations of Laurent series fields over fields of characteristic p. We compare the arithmetic and differential Swan conductors of rank one p-adic Galois representations of monomial fields with finite local monodromy. We also introduce a p-adic counterpart of monomial fields and explain generalizations of classical results to this setting, such as the overconvergence of p-adic Galois representations, and Berger’s construction of p-adic differential modules from de Rham ones.
The fake annuli introduced by Kedlaya are certain one-dimensional subannuli of p-adic polyannuli with multiple derivations. They are related to monomial fields, which are generalizations of Laurent series fields over fields of characteristic p. We compare the arithmetic and differential Swan conductors of rank one p-adic Galois representations of monomial fields with finite local monodromy. We also introduce a p-adic counterpart of monomial fields and explain generalizations of classical results to this setting, such as the overconvergence of p-adic Galois representations, and Berger’s construction of p-adic differential modules from de Rham ones.
