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arXiv · 2212.11374

Rees algebras and generalized depth-like conditions in prime characteristic

Alessandra Costantini·Kyle Maddox·Lance Edward Miller
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Abstract

In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing a depth-like invariant which captures as special cases Lyubeznik's F-depth and the generalized F-depth from Maddox-Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F-nilpotence deforms.

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Alessandra Costantini, Kyle Maddox, Lance Edward Miller. 2022-12-21. Rees algebras and generalized depth-like conditions in prime characteristic. https://doi.org/10.1002/mana.202200549

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