The asymptotic behavior of solid closure in mixed characteristic
Commutative Algebra
2007-05-23 v1
Abstract
We study how solid closure in mixed characteristic behaves after taking ultraproducts. The ultraproduct will be chosen so that we land in equal characteristic, and therefore can make a comparison with tight closure. As a corollary we get an asymptotic version of the Hochster-Roberts invariant theorem in dimension three: if is a mixed characteristic (cyclically) pure 3-dimensional local subring of a regular local ring , then is Cohen-Macaulay, provided the ramification of is large with respect to its dimension and residual characteristic, and with respect to the multiplicity of .
Cite
@article{arxiv.math/0409608,
title = {The asymptotic behavior of solid closure in mixed characteristic},
author = {Hans Schoutens},
journal= {arXiv preprint arXiv:math/0409608},
year = {2007}
}