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代数幾何学セミナー
過去の記録 ～04/25｜次回の予定｜今後の予定 04/26～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室 |
|---|---|
| 担当者 | 權業 善範、中村 勇哉、田中 公 |
2020年02月21日(金)
13:30-15:00 数理科学研究科棟(駒場) 370号室
いつもと曜日・時間・部屋が異なります
Jakub Witaszek 氏 (Michigan)
Keel's theorem and quotients in mixed characteristic (English)
http://www-personal.umich.edu/~jakubw/
いつもと曜日・時間・部屋が異なります
Jakub Witaszek 氏 (Michigan)
Keel's theorem and quotients in mixed characteristic (English)
[ 講演概要 ]
In trying to understand characteristic zero varieties one can apply a wide range of techniques coming from analytic methods such as vanishing theorems. More complicated though they are, positive characteristic varieties come naturally with Frobenius action which sometimes allows for imitating analytic proofs or even showing results which are false over complex numbers. Of all the three classes, the mixed characteristic varieties are the most difficult to understand as they represent the worst of both worlds: one lacks the analytic methods as well the Frobenius action.
What is key for many applications of Frobenius in positive characteristic (to birational geometry, moduli theory, constructing quotients, etc.) is the fact that every universal homeomorphism of algebraic varieties factors through a power of Frobenius. In this talk I will discuss an analogue of this fact (and applications thereof) in mixed characteristic.
[ 参考URL ]In trying to understand characteristic zero varieties one can apply a wide range of techniques coming from analytic methods such as vanishing theorems. More complicated though they are, positive characteristic varieties come naturally with Frobenius action which sometimes allows for imitating analytic proofs or even showing results which are false over complex numbers. Of all the three classes, the mixed characteristic varieties are the most difficult to understand as they represent the worst of both worlds: one lacks the analytic methods as well the Frobenius action.
What is key for many applications of Frobenius in positive characteristic (to birational geometry, moduli theory, constructing quotients, etc.) is the fact that every universal homeomorphism of algebraic varieties factors through a power of Frobenius. In this talk I will discuss an analogue of this fact (and applications thereof) in mixed characteristic.
http://www-personal.umich.edu/~jakubw/
