Remarks on the small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules

We show that any quasi-Gorenstein deformation of a 3-dimensional quasi-Gorenstein Buchsbaum local ring with I-invariant 1 admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings includes two instances of unique factorization domains constructed b...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2023-11, Vol.634, p.667-697
Main Authors: Shimomoto, Kazuma, Tavanfar, Ehsan
Format: Article
Language:English
Subjects:
Ample [formula omitted]-Weil divisors
Buchsbaum rings
Frobenius direct images
Frobenius pushforward
Graded rings/modules
Maximal Cohen-Macaulay modules
Quasi-Gorenstein rings
Small Cohen-Macaulay conjecture
Unique factorization domain
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that any quasi-Gorenstein deformation of a 3-dimensional quasi-Gorenstein Buchsbaum local ring with I-invariant 1 admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings includes two instances of unique factorization domains constructed by Marcel-Schenzel and by Imtiaz-Schenzel, respectively. Apart from this result, motivated by the small Cohen-Macaulay conjecture in prime characteristic, we examine a question about when the Frobenius pushforward F⁎e(M) of an R-module M comprises a maximal Cohen-Macaulay direct summand in both local and graded cases.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2023.06.045