饱和幂的渐近增长与epsilon重数
交换代数
2010-11-24 v4
摘要
研究了局部域R上模的饱和幂的渐近性质。在温和条件下，证明了当k趋于无穷时，模E的k次幂的饱和与E的k次幂之商除以k^{d+e-1}的极限存在。这里d是R的维数，e是E的秩。我们推断，在这些假设下，由Ulrich和Validashti定义为上极限的E的epsilon重数实际上作为极限存在。
引用
@article{arxiv.1009.4111,
title = {Asymptotic growth of saturated powers and epsilon multiplicity},
author = {Steven Dale Cutkosky},
journal= {arXiv preprint arXiv:1009.4111},
year = {2010}
}
备注
9 pages. In the revised version a typo ("n" changed to "k") is fixed in the statement of Corollary 1.3. A couple of new corollaries are added and some references are added. In the second revision (13 pages) some extensions from domains of depth \ge 2 are given to domains of dimension \ge 2