Tannaka duality for enhanced triangulated categories. I: Reconstruction
type: Item
instance of: scholarly article
title: Tannaka duality for enhanced triangulated categories. I: Reconstruction
zbMATH Open document ID: 1477.18031
DOI: 10.4171/JNCG/374
author: Jonathan Paul Pridham
published in: Journal of Noncommutative Geometry
publication date: 2021-06-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1812.10822
review text: Summary: 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.
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 14A30
Mathematics Subject Classification ID: 14F42
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16E45
zbMATH DE Number: 7358351
zbMATH Keywords: dg categories
zbMATH Keywords: Tannaka duality
zbMATH Keywords: motivic Galois groups
MaRDI profile type: Publication
arXiv ID: 1812.10822
cites work: The Hodge theoretic fundamental group and its cohomology
cites work: Q3509856
cites work: La réalisation étale et les opérations de Grothendieck
cites work: The Hopf algebra and the motivic Galois group of a field of characteristic zero. I
cites work: Q3758024
cites work: Relative categories: another model for the homotopy theory of homotopy theories
cites work: REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
cites work: ENHANCED TRIANGULATED CATEGORIES
cites work: Algebraic cycles and higher K-theory
cites work: A DG guide to Voevodsky's motives
cites work: Mixed Weil cohomologies
cites work: Triangulated Categories of Mixed Motives
cites work: Koszul-Morita duality
cites work: Q3977509
cites work: Théorie de Hodge. II. (Hodge theory. II)
cites work: Calculating simplicial localizations
cites work: Simplicial localizations of categories
cites work: Hodge cycles, motives, and Shimura varieties
cites work: DG quotients of DG categories.
cites work: Monoidal infinity category of complexes from Tannakian viewpoint
cites work: Mixed motives and algebraic cycles. I
cites work: Pro-Affine Algebraic Groups
cites work: Periods and Nori Motives
cites work: Tannakization in derived algebraic geometry
cites work: Q3978992
cites work: On the cyclic homology of exact categories
cites work: Q5489372
cites work: Rings with several objects
cites work: Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
cites work: The homotopy theory of strong homotopy algebras and bialgebras
cites work: Rational homotopy theory
cites work: Q3378982
cites work: A Quillen model structure on the category of dg categories
cites work: The homotopy theory of dg-categories and derived Morita theory
cites work: Moduli of objects in dg-categories
cites work: Cycles, Transfers, and Motivic Homology Theories. (AM-143)
OpenAlex ID: W3043746748
description: scientific article