Picard groups, weight structures, and (noncommutative) mixed motives
Algebraic Geometry
2016-01-05 v2 Algebraic Topology
Category Theory
K-Theory and Homology
Representation Theory
Abstract
We develop a general theory which enables the computation of the Picard group of a symmetric monoidal triangulated category, equipped with a weight structure, in terms of the Picard group of the associated heart. As an application, we compute the Picard group of several categories of motivic nature - mixed Artin motives, mixed Artin-Tate motives, motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras, noncommutative mixed motives of separable algebras - as well as the Picard group of the derived categories of symmetric ring spectra.
Cite
@article{arxiv.1512.09101,
title = {Picard groups, weight structures, and (noncommutative) mixed motives},
author = {Mikhail Bondarko and Goncalo Tabuada},
journal= {arXiv preprint arXiv:1512.09101},
year = {2016}
}
Comments
18 pages. Revised version