The Brauer group of Azumaya corings and the second cohomology group

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dc.creatorCaenepeel, S.
dc.creatorFemic, B.
dc.date2005-05-31
dc.date.accessioned2026-07-07T05:20:24Z
dc.date.available2026-07-07T05:20:24Z
dc.descriptionLet $R$ be a commutative ring. An Azumaya coring consists of a couple $(S,\Cc)$, with $S$ a faithfully flat commutative $R$-algebra, and an $S$-coring $\Cc$ satisfying certain properties. If $S$ is faithfully projective, then the dual of $\Cc$ is an Azumaya algebra. Equivalence classes of Azumaya corings form an abelian group, called the Brauer group of Azumaya corings. This group is canonically isomorphic to the second flat cohomology group. We also give algebraic interpretations of the second Amitsur cohomology group and the first Villamayor-Zelinsky cohomology group in terms of corings.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0505686
dc.identifierhttp://arxiv.org/abs/math/0505686
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75367
dc.subjectRings and Algebras
dc.subject16W30
dc.titleThe Brauer group of Azumaya corings and the second cohomology group
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