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 language | English (US) |
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Pages (from-to) | 21-42 |
Number of pages | 22 |
Journal | Pacific Journal of Mathematics |
Volume | 283 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
Keywords
- Derived categories
- Localizations
- Telescope conjecture
ASJC Scopus subject areas
- General Mathematics