On the vanishing of Tor of the absolute integral closure

Hans Schoutens

On the vanishing of Tor of the absolute integral closure

Commutative Algebra 2014-08-27 v1

Authors: Hans Schoutens

Abstract

Let $R$ be an excellent local domain of positive characteristic with residue field $k$ and let $R^+$ be its absolute integral closure. If $\text{Tor}^R_1(R^+,k)$ vanishes, then $R$ is Cohen-Macaulay, normal, F-rational and F-pure. If $R$ has at most an isolated singularity or has dimension at most two, then $R$ is regular.

Keywords

absolute integral closure tor vanishing excellent local domain positive characteristic cohen-macaulay

Cite

@article{arxiv.math/0304051,
  title  = {On the vanishing of Tor of the absolute integral closure},
  author = {Hans Schoutens},
  journal= {arXiv preprint arXiv:math/0304051},
  year   = {2014}
}

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