English

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.

Keywords

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

R2 v1 2026-06-21T23:51:17.143Z