English

Generically trivial derived categories

Representation Theory 2014-12-03 v2

Abstract

We study generic objects in triangulated categories and characterize the finite dimensional algebras AA such that the derived categories D(\ModA)D(\Mod A) are generically trivial. This is an analogue of a result of Crawley-Boevey for module categories. As a consequence, we show that D(\ModA)D(\Mod A) is generically trivial if and only if the category of perfect complexes Kb(\projA)K^b(\proj A) is locally finite.

Keywords

Cite

@article{arxiv.1308.2336,
  title  = {Generically trivial derived categories},
  author = {Han Zhe},
  journal= {arXiv preprint arXiv:1308.2336},
  year   = {2014}
}

Comments

10 pages

R2 v1 2026-06-22T01:07:27.769Z