Numerically finite hereditary categories with Serre duality
Category Theory
2015-01-14 v2 Algebraic Geometry
Abstract
Let A be an abelian hereditary category with Serre duality. We provide a classification of such categories up to derived equivalence under the additional condition that the Grothendieck group modulo the radical of the Euler form is a free abelian group of finite rank. Such categories are called numerically finite, and this condition is satisfied by the category of coherent sheaves on a smooth projective variety.
Cite
@article{arxiv.1304.0257,
title = {Numerically finite hereditary categories with Serre duality},
author = {Adam-Christiaan van Roosmalen},
journal= {arXiv preprint arXiv:1304.0257},
year = {2015}
}
Comments
41 pages, as accepted by the Transactions of the American Mathematical Society