Multiplicities and a dimension inequality for unmixed modules
交换代数
2007-05-23 v1
摘要
We prove the following result, which is motivated by the recent work of Kurano and Roberts on Serre's positivity conjecture. Assume that (R,m) is a local ring with finitely-generated module M such that R/ann(M) is quasi-unmixed and contains a field, and that p and q are prime ideals in the support of M such that p is analytically unramified, p+q is m-primary and e(M_p)=e(M). Then dim(R/p)+dim(R/q)\leq dim(M). We also prove a similar theorem in a special case of mixed characteristic. Finally, we provide several examples to explain our assumptions as well as an example of a noncatenary, local domain R with prime ideal p such that e(R_p)>e(R)=1.
引用
@article{arxiv.math/0212107,
title = {Multiplicities and a dimension inequality for unmixed modules},
author = {Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:math/0212107},
year = {2007}
}