固定维数局部环中 Hilbert-Kunz 重数的下界
交换代数
2008-04-07 v2
摘要
设 是一个维数为 且具有正素特征的 formally unmixed 局部环。我们考察具有较小 Hilbert-Kunz 重数（即接近 1）所带来的推论。特别地，我们证明了如果 不是正则环，则其 Hilbert-Kunz 重数存在一个严格大于 1 的下界，该下界仅依赖于 。
引用
@article{arxiv.0708.0537,
title = {Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension},
author = {Ian M. Aberbach and Florian Enescu},
journal= {arXiv preprint arXiv:0708.0537},
year = {2008}
}
备注
14 pages, to appear in Michigan Math Journal; a number of corrections were performed according to the referee's comments, including a weakening of Corollary 3.10 which led to a small change in the lower bound in Theorem 4.12