On local rings without small Cohen-Macaulay algebras in mixed characteristic
Commutative Algebra
2026-01-05 v5 Algebraic Geometry
Abstract
For any , by deformation theory of schemes, we present examples of (complete or excellent) -dimensional mixed characteristic normal local domains admitting no small Cohen-Macaulay algebra, but admitting instances of small (maximal) Cohen-Macaulay modules. It is also shown that a graded normal domain over a field whose Proj is an Abelian variety admits a graded small (maximal) Cohen-Macaulay module.
Keywords
Cite
@article{arxiv.2109.12700,
title = {On local rings without small Cohen-Macaulay algebras in mixed characteristic},
author = {Kazuma Shimomoto and Ehsan Tavanfar},
journal= {arXiv preprint arXiv:2109.12700},
year = {2026}
}
Comments
Accepted for publication in Mathematical Research Letters. This is different from the published version. We decided to let Proposition 2.4, Remark 2.5 and comments on crystalline cohomology after Theorem 3.7 remain for the interested readers