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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 |
2021/06/23
17:00-18:00 Online
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
[ Abstract ]
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
