Unbounded Algebraic Derivators
Category Theory
2024-05-17 v3 Algebraic Geometry
Representation Theory
Abstract
We show that the unbounded derived category of a Grothendieck category with enough projective objects is the base category of a derivator whose category of diagrams is the full 2-category of small categories. With this structure, we give a description of the localization functor associated to a specialization closed subset of the spectrum of a commutative noetherian ring. In addition, using the derivator of modules, we prove some basic theorems of group cohomology for complexes of representations over an arbitrary base ring.
Cite
@article{arxiv.2111.05918,
title = {Unbounded Algebraic Derivators},
author = {Leovigildo Alonso and Beatriz Álvarez and Ana Jeremías},
journal= {arXiv preprint arXiv:2111.05918},
year = {2024}
}
Comments
V3, final version, V2 Corrected proof of Proposition 2.10 and several other improvements. 32 pages