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The relative Brauer group and generalized cyclic crossed products for a ramified covering
- Source :
- Journal of Algebra. 450:1-58
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- Let T/A be an integral extension of noetherian integrally closed integral domains whose quotient field extension is a finite cyclic Galois extension. Let S/R be a localization of this extension which is unramified. Using a generalized cyclic crossed product construction it is shown that certain reflexive fractional ideals of T with trivial norm give rise to Azumaya R-algebras that are split by S. Sufficient conditions on T/A are derived under which this construction can be reversed and the relative Brauer group of S/R is shown to fit into the exact sequence of Galois cohomology associated to the ramified covering T/A. Many examples of affine algebraic varieties are exhibited for which all of the computations are carried out.
- Subjects :
- Discrete mathematics
Pure mathematics
Algebra and Number Theory
Galois cohomology
Group cohomology
010102 general mathematics
Galois group
Abelian extension
01 natural sciences
010101 applied mathematics
Mathematics::K-Theory and Homology
Field extension
Galois extension
0101 mathematics
Brauer group
Field norm
Mathematics
Subjects
Details
- ISSN :
- 00218693
- Volume :
- 450
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi...........3c954785adbecf3224b3b218358d7578