Antieau, B. and Stevenson, G. (2016) Derived categories of representations of small categories over commutative noetherian rings. Pacific Journal of Mathematics, 283(1), pp. 21-42. (doi: 10.2140/pjm.2016.283.21)
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Abstract
We study the derived categories of small categories over commutative noetherian rings. Our main result is a parametrization of the localizing subcategories 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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Stevenson, Dr Gregory |
| Authors: | Antieau, B., and Stevenson, G. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Pacific Journal of Mathematics |
| Publisher: | Mathematical Sciences Publishers |
| ISSN: | 0030-8730 |
| ISSN (Online): | 0030-8730 |
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