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Liftable derived equivalences and objective categories
- Source :
- Bulletin of the London Mathematical Society, 52 (2020), 816-834
- Publication Year :
- 2019
-
Abstract
- We give two proofs to the following theorem and its generalization: if a finite dimensional algebra $A$ is derived equivalent to a smooth projective scheme, then any derived equivalence between $A$ and another algebra $B$ is standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain projective scheme is triangle-objective, that is, any triangle autoequivalence on it, which preserves the the isomorphism classes of complexes, is necessarily isomorphic to the identity functor.
Details
- Database :
- arXiv
- Journal :
- Bulletin of the London Mathematical Society, 52 (2020), 816-834
- Publication Type :
- Report
- Accession number :
- edsarx.1902.06033
- Document Type :
- Working Paper