Abstract
In this paper we begin studying tannakian constructions in ∞-categories and combine them with the theory of motivic categories developed by Hanamura, Levine, and Voevodsky. This paper is the first in a series of papers. For the purposes above, we first construct a derived affine group scheme and its representation category from a symmetric monoidal ∞-category, which we shall call the tannakization of a symmetric monoidal ∞-category. It can be viewed as an ∞-categorical generalization of work of Joyal-Street and Nori. Next we apply it to the stable ∞-category of mixed motives equipped with the realization functor of a mixed Weil cohomology. We construct a derived motivic Galois group which represents the automorphism group of the realization functor, and whose representation category satisfies an appropriate universal property. As a consequence, we construct an underived motivic Galois group of mixed motives, which is a pro-algebraic group and has nice properties. Also, we present basic properties of derived affine group schemes in the Appendix.
Original language | English |
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Pages (from-to) | 642-700 |
Number of pages | 59 |
Journal | Journal of K-Theory |
Volume | 14 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2014 Jul 8 |
Keywords
- motives
- symmetric monoidal ∞-category
- tannakian construction
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology