Tannaka duality for enhanced triangulated categories II: $t$-structures and homotopy types

Abstract

We consider the effect of $t$-structures on the Tannaka duality theory for dg categories developed in our previous paper. We associate non-negative dg coalgebras $C$ to dg functors on the hearts of $t$-structures, and relate dg $C$-comodules to the original dg category. We give several applications for pro-algebraic homotopy types associated to various cohomology theories, and for motivic Galois groups.

30 pages; v2 has reorganised section 3, with new results on motives (Examples 3.17 and 3.27); v3 further detail for motivic examples, and appendix added; v4 corrections in section 3.1, and to motivic examples; v5 expanded monoidal section; v6 consists of sections 3 & 4 from v5 (sections 1 & 2 now form a separate paper)

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