# nLab Schneider's theorem

The Schneider’s descent theorem is a noncommutative affine analogue of the descent along a torsor where the structure group is also replaced by a Hopf algebra.
In a left-right version, it says that given a Hopf algebra $H$ and a faithfully flat Hopf-Galois extension $U\hookrightarrow E$ (where $E$ is a right $H$-comodule algebra), the category of left-right relative Hopf modules ${}_E\mathcal{M}^H$ is equivalent to the category of left $U$-modules ${}_U \mathcal{M}$. The adjoint equivalence is given canonically…

• Hans-Jürgen Schneider, Principal homogeneous spaces for arbitrary Hopf algebras, Israel J. Math. 72 (1990), no. 1-2, 167–195 MR92a:16047 doi
• Z. Škoda, Some equivariant constructions in noncommutative algebraic geometry Georgian Mathematical Journal 16 (2009), No. 1, 183–202, arXiv:0811.4770 MR2011b:14004
• A. Ardizzoni, G. Böhm, C. Menini, A Schneider type theorem for Hopf algebroids, J. Algebra 318 (2007), no. 1, 225–269 MR2008j:16103 doi math.QA/0612633 (arXiv version is unified, corrected); Corrigendum, J. Algebra 321:6 (2009) 1786-1796 MR2010b:16060 doi

Last revised on November 30, 2012 at 20:12:03. See the history of this page for a list of all contributions to it.