The Brauer Group of a Local Field

Algebra ◽  
2007 ◽  
pp. 223-238
Keyword(s):  
Local Field ◽  
Brauer Group

On the Brauer group of a two-dimensional local field

2007 ◽  
Vol 81 (5-6) ◽  
pp. 753-756
Author(s):  
M. A. Dubovitskaya
Keyword(s):  
Local Field ◽  
Brauer Group ◽  
Two Dimensional

Computation of the norm factor group over Henselian fields and tame Brauer group of generalized local fields

2015 ◽  
Vol 14 (08) ◽  
pp. 1550134
Author(s):  
Mehran Motiee
Keyword(s):  
Abelian Group ◽  
Local Field ◽  
Finite Extension ◽  
Factor Group ◽  
Local Fields ◽  
Brauer Group ◽  
Divisible Abelian Group

Let F be a Henselian field. For a finite extension K of F, the norm factor group [Formula: see text] is computed. As an application, structure of the tame Brauer group of a generalized local field is determined. In particular, we observe that every torsion divisible abelian group is realizable as the tame Brauer group of a generalized local field.

scholarly journals Groups of components of Néron models of Jacobians and Brauer groups

2015 ◽  
Vol 11 (02) ◽  
pp. 621-629 ◽  
Author(s):  
Saikat Biswas
Keyword(s):  
Local Field ◽  
Brauer Group ◽  
Brauer Groups ◽  
Component Group ◽  
Neron Models ◽  
Néron Models

Let X be a proper, smooth, and geometrically connected curve over a non-archimedean local field K. In this paper, we relate the component group of the Néron model of the Jacobian of X to the Brauer group of X.

scholarly journals More on the Schur group of a commutative ring

1985 ◽  
Vol 8 (2) ◽  
pp. 275-282 ◽  
Author(s):  
R. A. Mollin
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Homomorphic Image ◽  
Group Ring ◽  
Local Field ◽  
Natural Generalization ◽  
Brauer Group ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

The Schur group of a commutative ring,R, with identity consists of all classes in the Brauer group ofRwhich contain a homomorphic image of a group ringRGfor some finite groupG. It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur exponent of a ring which equals the well-known Schur index in the global or local field case.

scholarly journals More on the Schur group of a commutative ring

1985 ◽  
Vol 8 (3) ◽  
pp. 513-520
Author(s):  
R. A. Mollin
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Homomorphic Image ◽  
Group Ring ◽  
Local Field ◽  
Natural Generalization ◽  
Brauer Group ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

The Schur group of a commutative ring,R, with identity consists of all classes in the Brauer group ofRwhich contain a homomorphic image of a group ringRGfor some finite groupG. It is the purpose of this article to continue an investigation of this group which was introduced in earler work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur exponent of a ring which equals the well-known Schur index in the global or local field case.

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