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math.AC2025
Variants on Frobenius Intersection Flatness and Applications to Tate Algebras
Rankeya Datta, Neil Epstein, Karl Schwede +1
The theory of singularities defined by Frobenius has been extensively developed for -finite rings and for rings that are essentially of finite type over excellent local rings. H…
math.AC2025
Closure operations induced via resolutions of singularities in characteristic zero
Neil Epstein, Peter M. McDonald, Rebecca R. G. +1
Using the fact that the structure sheaf of a resolution of singularities, or regular alteration, pushes forward to a Cohen-Macaulay complex in equal characteristic zero with a diff…
math.AC2025
A common framework for test ideals, closure operations, and their duals
Neil Epstein, Rebecca R. G., Janet Vassilev
Closure operations such as tight and integral closure and test ideals have appeared frequently in the study of commutative algebra. This articles serves as a survey of the authors'…