Year: 2026
Type: preprint
Abstract: Bertin (1972) defined regularity for coherent local rings, and Knaf (2004) studied the property for a local ring $A$ essentially finitely presented over a valuation ring $V$. We discuss several properties of this notion of regularity for such $A$, obtaining results parallel to results for regularity of Noetherian local rings. We include classical and modern topics: openness of loci, perfectoid big Cohen--Macaulay algebras, and cotangent complexes. We also give an application to Noetherian rings, showing a version of Kodaira's vanishing theorem in large enough residue characteristics.
Source: arXiv (Cornell University)
Author: Lyu, Shiji
Institution: University of Illinois Chicago
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7147728913
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