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過去の記録 ～04/26｜次回の予定｜今後の予定 04/27～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2021年06月23日(水)
17:00-18:00 オンライン開催
今井 湖都 氏 (東京大学大学院数理科学研究科)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
今井 湖都 氏 (東京大学大学院数理科学研究科)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
[ 講演概要 ]
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.
