Tannaka duality for enhanced triangulated categories I: reconstruction

J. Pridham
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引用次数: 1

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.
增强三角分类I的Tannaka对偶性:重建
我们发展了dg范畴的Tannaka对偶理论。对于有限维复形中的任意dg函子,我们通过一个Hochschild同调构造关联了一个dg协代数C$。当dg函子是忠实的,这给出了$\mathcal{a}$-模和$C$-模的派生的dg范畴之间的拟等价。当$\mathcal{A}$是Morita纤维(即一个幂等完备的预三角化范畴)时,它因此拟等价于紧模$C$-的派生dg范畴。我们给出了动机伽罗瓦群的几种应用。
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