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Homotopic Hopf-Galois extensions revisited
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in arXiv:0902.3393v2 [math.AT], in light of the homotopical Morita theory of comodules established in arXiv:1411.6517 [math.AT]. 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 forthcoming work of the second author and Karpova. 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. 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.

National Category
Algebra and Logic Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-111903OAI: oai:DiVA.org:su-111903DiVA: diva2:777046
Available from: 2015-01-08 Created: 2015-01-08 Last updated: 2016-01-29Bibliographically approved

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