代数幾何学セミナー

過去の記録 ~01/29次回の予定今後の予定 01/30~

開催情報 火曜日 10:30~11:30 or 12:00 数理科学研究科棟(駒場) ハイブリッド開催/002号室
担当者 權業 善範・中村 勇哉・田中公

2022年11月01日(火)

10:30-12:00   数理科学研究科棟(駒場) ハイブリッド開催/002号室
河上龍郎 氏 (京大数学教室)
Extendability of differential forms via Cartier operators (Japanese)
[ 講演概要 ]
For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.
In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.
For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.