Arithmetic deformations of F-singularities

Abstract: F-singularities are singularities in positive characteristic defined via the Frobenius map. In the first half of the talk, I will survey a connection between F-singularities and singularities in complex birational geometry. In the second half of the talk, I will present a new application of Ma-Schwede’s theory of singularities in mixed characteristic. They proved that a Q-Gorenstein affine domain over a field of characteristic zero has log terminal singularities if its mod p reduction is F-regular for one single prime p. I will discuss the analog of their result for log canonical singularities. This talk is based on joint work with Kenta Sato.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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