Dimensions of triangulated categories with respect to subcategories
Representation Theory
2013-10-01 v2 Commutative Algebra
Rings and Algebras
Abstract
This paper introduces the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings.
Keywords
Cite
@article{arxiv.1204.6421,
title = {Dimensions of triangulated categories with respect to subcategories},
author = {Takuma Aihara and Tokuji Araya and Osamu Iyama and Ryo Takahashi and Michio Yoshiwaki},
journal= {arXiv preprint arXiv:1204.6421},
year = {2013}
}
Comments
16 pages, to appear in J. Algebra