Derived categories of representations of small categories over commutative noetherian rings

Benjamin Antieau, Greg Stevenson

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the derived categories of small categories over commutative noe-therian rings. Our main result is a parametrization of the localizing subcat-egories in terms of the spectrum of the ring and the localizing subcategories over residue fields. In the special case of representations of Dynkin quivers over a commutative noetherian ring, we give a complete description of the localizing subcategories of the derived category and a complete description of the thick subcategories of the perfect complexes. We also show that the telescope conjecture holds in this setting and we present some results concerning the telescope conjecture more generally.

Original languageEnglish (US)
Pages (from-to)21-42
Number of pages22
JournalPacific Journal of Mathematics
Volume283
Issue number1
DOIs
StatePublished - 2016
Externally publishedYes

Keywords

  • Derived categories
  • Localizations
  • Telescope conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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