DOCUMENTA MATHEMATICA, Vol. 22 (2017), 45-66

Mikhail Bondarko and Gonçalo Tabuada

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

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.

2010 Mathematics Subject Classification: 14A22, 14C15, 14F42, 18E30, 55P43

Keywords and Phrases: Picard group, weight structure, mixed motives, motivic spectra, noncommutative mixed motives, symmetric ring spectra, noncommutative algebraic geometry

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