JournalsdmVol. 22pp. 45–66

Picard Groups, Weight Structures, and (noncommutative) Mixed Motives

  • Mikhail Bondarko

    Universitetsky pr. 28, St. Petersburg State University, the Faculty of Higher Algebra and Number Theory, 198504 St. Petersburg, Russia

  • Gonçalo Tabuada

    Department of Mathematics, MIT Cambridge, MA 02139, USA; Departamento de Matemática, FCT-UNL Portugal; CMA Centro de Matemática e Aplicações, Portugal
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Abstract

We develop a general theory which, under certain assumptions, 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, bootstrap motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras – as well as the Picard group of certain derived categories of symmetric ring spectra.

Cite this article

Mikhail Bondarko, Gonçalo Tabuada, Picard Groups, Weight Structures, and (noncommutative) Mixed Motives. Doc. Math. 22 (2017), pp. 45–66

DOI 10.4171/DM/559