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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 211A: Seminar in Algebra
Jack J Garzella
UC San Diego
Quasi-F-splitness and F-pure thresholds of hypersurface rings
Abstract:
The theory of F-singularities uses the Frobenius morphism to measure how "singular" a ring is, that is, how far it is from being a regular ring. We describe two ways to measure singularities using frobenius, respectively called the quasi-F-split height and the F-pure threshold. We describe a relationship between these two invariants, which is latent in the literature, under very specific assumptions. The proof of this statement uses sophisticated geometric machinery (including deformation theory and crystalline cohomology). We then describe a more general proof, joint with Jagathese, that uses only algebra.
November 24, 2025
3:00 PM
APM 7321
Research Areas
Algebra Algebraic Geometry****************************
