On the vanishing of Tor of the absolute integral closure

Details On the vanishing of Tor of the absolute integral closure On the vanishing of Tor of the absolute integral closure

2003-04-03

arxiv.org/abs/math/0304051v1

J. Algebra 275 (2004), 567-574

Mathematics

Commutative Algebra

Scientific paper

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.

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