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Homotopic Hopf-Galois extensions revisited
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22018 (English)In: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 12, no 1, p. 107-155Article in journal (Refereed) Published
Abstract [en]

In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in [9], in light of the homotopical Morita theory of comodules established in [3]. We generalize the theory to a relative framework, which we believe is new even in the classical context and which is essential for treating the Hopf-Galois correspondence in [19]. We study in detail homotopic Hopf-Galois extensions of differential graded algebras over a commutative ring, for which we establish a descent-type characterization analogous to the one Rognes provided in the context of ring spectra [26]. An interesting feature in the differential graded setting is the close relationship between homotopic Hopf-Galois theory and Koszul duality theory. We show that nice enough principal fibrations of simplicial sets give rise to homotopic Hopf-Galois extensions in the differential graded setting, for which this Koszul duality has a familiar form.

Place, publisher, year, edition, pages
2018. Vol. 12, no 1, p. 107-155
Keywords [en]
Hopf-Galois extension, descent, Morita theory, model category
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-156030DOI: 10.4171/JNCG/272ISI: 000428804300004OAI: oai:DiVA.org:su-156030DiVA, id: diva2:1203721
Available from: 2018-05-04 Created: 2018-05-04 Last updated: 2018-05-04Bibliographically approved

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