On the vanishing of Tor of the absolute integral closure
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 TorR1(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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