On quasi-Frobenius-split singularities

Abstract: In algebraic geometry of positive characteristic, singularities defined by the Frobenius map, including the notion of Frobenius-splitting, have played a crucial role. Yobuko recently introduced the notion of quasi-F-splitting and F-split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that F-split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. This notion is defined for purely positive characteristic varieties, but the ring of Witt vectors, which is a mixed characteristic object, makes an essential role in the definition.

In this talk, I present several criteria for quasi-F-splitting and their applications. This talk is based on joint research with T. Kawakami, H. Tanaka, J. Witaszek, F. Yobuko, and S. Yoshikawa.

Mathematics

Audience: researchers in the topic

CUHK Number Theory Online Seminar