The derived-discrete algebras and standard equivalences

Chen, Xiaowu; Zhang, Chao

doi:10.1016/j.jalgebra.2019.01.031

Cited by 3 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is a well‐known open question [20] whether any derived equivalence is standard , that is, isomorphic to the derived tensor functor by a two‐sided tilting complex. We refer to [8, Introduction] for known cases where the question is answered affirmatively.…”

Section: Introductionmentioning

confidence: 99%

Liftable derived equivalences and objective categories

Chen

2020

Bull. London Math. Soc.

View full text Add to dashboard Cite

We give two proofs of the following theorem and a partial 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 class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor.

show abstract

Section: Introductionmentioning

confidence: 99%