Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties

Details Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties

2004-06-22

arxiv.org/abs/math/0406436v3

Mathematics

Rings and Algebras

42 pages

Scientific paper

El Kaoutit and G\'omez Torrecillas introduced comatrix corings, generalizing Sweedler's canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They also introduced Galois corings, as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita context to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.

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