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 language | English |
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Publisher | ArXiv |
Publication status | Published - 19 Sep 2012 |
Keywords
- math.RT
- math.AC
- math.AG
- 14J17, 13C14, 18E30, 16E65