Resolutions in factorization categories
Category Theory
2014-05-14 v2 Commutative Algebra
Algebraic Geometry
Abstract
Generalizing Eisenbud's matrix factorizations, we define factorization categories. Following work of Positselski, we define their associated derived categories. We construct specific resolutions of factorizations built from a choice of resolutions of their components. We use these resolutions to lift fully-faithfulness statements from derived categories of Abelian categories to derived categories of factorizations and to construct a spectral sequence computing the morphism spaces in the derived categories of factorizations from Ext-groups of their components in the underlying Abelian category.
Cite
@article{arxiv.1212.3264,
title = {Resolutions in factorization categories},
author = {Matthew Ballard and Dragos Deliu and David Favero and M. Umut Isik and Ludmil Katzarkov},
journal= {arXiv preprint arXiv:1212.3264},
year = {2014}
}
Comments
v2: Expanded further for enjoyment. 41 pages. v1: 24 pages, expanded from a section in arXiv:1203.6643, comments welcome