关于混合特征下无小Cohen-Macaulay代数的局部环
交换代数
2026-01-05 v5 代数几何
摘要
对于任意 ，通过概形的形变理论，我们给出了（完备或优的） 维混合特征正规局部整环的例子，它们不承认小Cohen-Macaulay代数，但承认小（极大）Cohen-Macaulay模的实例。同时还证明，一个域上的分次正规整环，如果其Proj是阿贝尔簇，则承认一个分次小（极大）Cohen-Macaulay模。
引用
@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}
}
备注
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