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A dimension inequality for Cohen-Macaulay rings

Authors:	Sean Sather-Wagstaff

Institution:	Department of Mathematics, University of Utah, 155 S. 1400 E., Salt Lake City, Utah 84112-0090

Abstract:	The recent work of Kurano and Roberts on Serre's positivity conjecture suggests the following dimension inequality: for prime ideals $\mathfrak{p}$ and $\mathfrak{q}$ in a local, Cohen-Macaulay ring $(A,\mathfrak{n})$ such that $e(A_{\mathfrak{p}})=e(A)$ we have $\dim(A/\mathfrak{p})+\dim(A/\mathfrak{q})\leq\dim(A)$ . We establish this dimension inequality for excellent, local, Cohen-Macaulay rings which contain a field, for certain low-dimensional cases and when $R/\mathfrak{p}$ is regular.

Keywords:	Intersection dimension intersection multiplicities multiplicities

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