Equimultiplicity Theory of Strongly $F$-regular rings

Published 4 Jun 2019 in math.AC | (1906.01162v2)

Abstract: We explore the equimultiplicity theory of the $F$-invariants Hilbert--Kunz multiplicity, $F$-signature, Frobenius Betti numbers, and Frobenius Euler characteristic over strongly $F$-regular rings. Techniques introduced in this article provide a unified approach to the study of these $F$-invariants under localization and as measurements of singularities.

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