Introduction to Derived Categories
Abstract
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was established. This "new" homological algebra, of derived categories and derived functors between them, provides a significantly richer and more flexible machinery than the "old" homological algebra. For instance, the important concepts of dualizing complex and tilting complex do not exist in the "old" homological algebra. This paper is an edited version of the notes for a two-lecture minicourse given at MSRI in January 2013. Sections 1-5 are about the general theory of derived categories, and the material is taken from my manuscript "A Course on Derived Categories" (available online). Sections 6-9 are on more specialized topics, leaning towards noncommutative algebraic geometry.
Cite
@article{arxiv.1501.06731,
title = {Introduction to Derived Categories},
author = {Amnon Yekutieli},
journal= {arXiv preprint arXiv:1501.06731},
year = {2015}
}
Comments
18 pages, to appear in MSRI volume on Noncommutative Algebraic Geometry