Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms

Details Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms

2011-08-30

arxiv.org/abs/1108.5797v1

Mathematics

Rings and Algebras

16 pages

Scientific paper

The aim of this paper is threefold: first, to prove that the endomorphism ring associated to a pure subring of a regular local ring is a noncommutative crepant resolution if it is maximal Cohen-Macaulay; second, to see that in that situation, a different, but Morita equivalent, noncommutative crepant resolution can be constructed by using Frobenius morphisms; finally, to study the relation between Frobenius morphisms of noncommutative rings and the finiteness of global dimension. As a byproduct, we will obtain a result on wild quotient singularities: If the smooth cover of a wild quotient singularity is unramified in codimension one, then the singularity is not strongly F-regular.

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