Unbounded derived categories and the finitistic dimension conjecture
Representation Theory
2018-04-27 v1 Rings and Algebras
Abstract
We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a non-Noetherian commutative ring where they don't, but prove that they do for any Noetherian commutative ring. For non-commutative finite dimensional algebras the question is open, and we prove that if injectives generate for such an algebra, then the finitistic dimension conjecture holds for that algebra.
Cite
@article{arxiv.1804.09801,
title = {Unbounded derived categories and the finitistic dimension conjecture},
author = {Jeremy Rickard},
journal= {arXiv preprint arXiv:1804.09801},
year = {2018}
}