Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, Feb 28, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
@ 4:30 pm, Virtual
Tatsuro Kawakami
Kyoto University
Title |
Extendability of differential forms via Cartier operators Note the unusual time! |
Abstract |
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. |
Algebraic Geometry