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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: S. Caenepeel, E. De Groot and J. Vercruysse
Journal: Trans. Amer. Math. Soc. 359 (2007), 185-226
MSC (2000): Primary 16W30
Published electronically: July 21, 2006
MathSciNet review: 2247888
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Abstract: El Kaoutit and Gómez-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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Additional Information

S. Caenepeel
Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
Email: scaenepe@vub.ac.be

E. De Groot
Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
Email: edegroot@vub.ac.be

J. Vercruysse
Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
Email: joost.vercruysse@vub.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03857-8
PII: S 0002-9947(06)03857-8
Keywords: Galois coring, comatrix coring, descent theory, Morita context
Received by editor(s): March 3, 2004
Received by editor(s) in revised form: October 19, 2004
Published electronically: July 21, 2006
Article copyright: © Copyright 2006 American Mathematical Society