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Abstract
Let R be an isolated Gorenstein singularity with a noncommutative resolution A=EndR(R⊕M)A=EndR(R⊕M). In this paper, we show that the relative singularity category ΔR(A)ΔR(A) of A has a number of pleasant properties, such as being Homfinite. Moreover, it determines the classical singularity category Dsg(R)Dsg(R) of Buchweitz and Orlov as a certain canonical quotient category. If R has finite CM type, which includes for example Kleinian singularities, then we show the much more surprising result that Dsg(R)Dsg(R) determines ΔR(Aus(R))ΔR(Aus(R)), where Aus(R)Aus(R) is the corresponding Auslander algebra. The proofs of these results use dg algebras, A∞A∞ Koszul duality, and the new concept of dg Auslander algebras, which may be of independent interest..
Original language  English 

Pages (fromto)  9731021 
Number of pages  45 
Journal  Advances in Mathematics 
Volume  301 
Early online date  21 Jul 2016 
DOIs  
Publication status  Published  1 Oct 2016 
Keywords
 math.AG
 math.AC
 math.CT
 math.RT
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Dive into the research topics of 'Relative singularity categories I: Auslander resolutions'. Together they form a unique fingerprint.Projects
 1 Finished

Homological interactions between singularity theory, representation theory and algebraic geometry
Kalck, M.
1/04/14 → 31/08/17
Project: Research