Frobenius categories, Gorenstein algebras and rational surface singularities

Osamu Iyama, Martin Kalck, Michael Wemyss, Dong Yang

Research output: Working paper

Abstract

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result to the Frobenius category of special Cohen-Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga-Gorenstein rings of finite GP type. We also apply our method to representation theory, obtaining Auslander-Solberg and Kong type results.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 19 Sep 2012

Keywords

  • math.RT
  • math.AC
  • math.AG
  • 14J17, 13C14, 18E30, 16E65

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