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arXiv · 1804.09801

Unbounded derived categories and the finitistic dimension conjecture

Jeremy Rickard
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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.

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Jeremy Rickard. 2018-04-25. Unbounded derived categories and the finitistic dimension conjecture. https://arxiv.org/abs/1804.09801

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