JournalsjncgVol. 14, No. 2pp. 591–637

Tannaka duality for enhanced triangulated categories I: reconstruction

  • Jonathan P. Pridham

    University of Edinburgh, UK
Tannaka duality for enhanced triangulated categories I: reconstruction cover

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Abstract

We develop Tannaka duality theory for dg categories. To any dg functor from a dg category A\mathcal A to finite-dimensional complexes, we associate a dg coalgebra CC via a Hochschild homology construction. When the dg functor is faithful, this gives a quasi-equivalence between the derived dg categories of A\mathcal A-modules and of CC-comodules. When A\mathcal A is Morita fibrant (i.e. an idempotent-complete pre-triangulated category), it is thus quasi-equivalent to the derived dg category of compact CC-comodules. We give several applications for motivic Galois groups.

Cite this article

Jonathan P. Pridham, Tannaka duality for enhanced triangulated categories I: reconstruction. J. Noncommut. Geom. 14 (2020), no. 2, pp. 591–637

DOI 10.4171/JNCG/374