Work

Rees algebras and generalized depth‐like conditions in prime characteristic

Year: 2023

Type: article

Abstract: In this paper, 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.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.202200549

Authors: Alessandra Costantini, Kyle Maddox, Lance Edward Miller

Institutions: Oklahoma State University, University of Kansas, University of Arkansas at Fayetteville

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4386460437

FWCI:

Cites: 23

Cited by:

Related to: 10