Homotopic Hopf-Galois extensions revisited
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
Alexander Berglund
K. Hess
Akses Cepat
- Tahun Terbit
- 2014
- Bahasa
- en
- Total Sitasi
- 3×
- Sumber Database
- Semantic Scholar
- DOI
- 10.4171/JNCG/272
- Akses
- Open Access ✓