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arXiv · 1507.00456

Derived categories of representations of small categories over commutative noetherian rings

Benjamin Antieau·Greg Stevenson
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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, a complete description of the thick subcategories of the perfect complexes and show the telescope conjecture holds. We also present some results concerning the telescope conjecture more generally.

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Benjamin Antieau, Greg Stevenson. 2015-07-02. Derived categories of representations of small categories over commutative noetherian rings. https://doi.org/10.2140/pjm.2016.283.21

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