Frobenius categories, Gorenstein algebras and rational surface singularities. (28th October 2014)

• Record Type: Journal Article
• Authors: Kalck, Martin; Iyama, Osamu; Wemyss, Michael; Yang, Dong
• Is Part Of: Compositio mathematica. Volume 151:Number 3(2015:May)
• Page Start: 502
• Page End: 534
• Publication Date: 2014-10-28
• Subjects: 14J17, -- 13C14, -- 18E30, -- 16E65 (primary); Frobenius categories, -- Iwanaga–Gorenstein algebras, -- Gorenstein-projective modules, -- Cohen–Macaulay modules, -- non-commutative resolutions, -- singularity categories, -- rational surface singularities; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X14007647
• Languages: English
• ISSNs: 0010-437X

Abstract

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 Gorenstein projective type. We also apply our method to representation theory, obtaining Auslander–Solberg and Kong type results.