A Characterization of F-Regularity in Terms of F-Purity

  • Richard Fedder
  • Kei-Ichi Watanabe
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 15)

Abstract

In recent years, some very interesting theorems have been proven independently using complex analytic techniques or, alternatively, using reduction to characteristic p techniques (relying on special properties of the Frobenius homomorphism). In particular, Hochster and Roberts [12] proved that the ring RG of invariants of a group G acting on a regular ring R is necessarily Cohen-Macaulay by an argument which exploits the fact that RG is a direct summand of R in characteristic 0 and that, therefore, after reduction to characteristic p, the Frobenius homomorphism is especially well-behaved for “almost all p”. Not long after, using the Grauert-Riemenschneider vanishing theorem, Boutôt [1] proved an even stronger result— in the affine and analytic cases, a direct summand (in characteristic 0) of a ring with rational singularity necessarily has a rational singularity.

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Richard Fedder
    • 1
    • 2
  • Kei-Ichi Watanabe
    • 1
    • 2
  1. 1.ColumbiaUSA
  2. 2.Department of Mathematical SciencesTokai UniversityHiratsukaJapan

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