Unbounded derived categories and the finitistic dimension conjecture

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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.
Original languageEnglish
Article number106735
Number of pages21
JournalAdvances in Mathematics
Volume354
Early online date23 Jul 2019
DOIs
Publication statusPublished - 1 Oct 2019

Keywords

  • Derived categories
  • Finite dimensional algebras
  • Finitistic dimension conjecture

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