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Mathematics > K-Theory and Homology

arXiv:1812.10822 (math)
[Submitted on 27 Dec 2018]

Title:Tannaka duality for enhanced triangulated categories I: reconstruction

Authors:J.P.Pridham
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Abstract:We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is faithful, this gives a quasi-equivalence between the derived dg categories of $\mathcal{A}$-modules and of $C$-comodules. When $\mathcal{A}$ is Morita fibrant (i.e. an idempotent-complete pre-triangulated category), it is thus quasi-equivalent to the derived dg category of compact $C$-comodules. We give several applications for motivic Galois groups.
Comments: 35 pp. This is the 1st half of arXiv:1309.0637v5, which has now been split. To appear in JNCG
Subjects: K-Theory and Homology (math.KT); Algebraic Geometry (math.AG); Algebraic Topology (math.AT)
Cite as: arXiv:1812.10822 [math.KT]
  (or arXiv:1812.10822v1 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.1812.10822

Submission history

From: Jonathan Pridham [view email]
[v1] Thu, 27 Dec 2018 20:51:15 UTC (45 KB)
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