Brauer groups of curves and unramified, central simple algebras over their function fields

2000 ◽  
Vol 102 (3) ◽  
pp. 4071-4133
Author(s):  
V. Yanchevskii ◽  
G. Margolin ◽  
U. Rehmann
Keyword(s):  
Function Fields ◽  
Brauer Groups ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

scholarly journals Splitting of Algebras by Function Fields of One Variable

1966 ◽  
Vol 27 (2) ◽  
pp. 625-642 ◽  
Author(s):  
Peter Roquette
Keyword(s):  
Tensor Product ◽  
Function Fields ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Field Extension ◽  
Brauer Group ◽  
Central Simple Algebras ◽  
Natural Mapping ◽  
Simple Algebras ◽  
Central Simple

Let K be a field and (K) the Brauer group of K. It consists of the similarity classes of finite central simple algebras over K. For any field extension F/K there is a natural mapping (K) → (F) which is obtained by assigning to each central simple algebra A/K the tensor product which is a central simple algebra over F. The kernel of this map is the relative Brauer group (F/K), consisting of those A ∈(K) which are split by F.

scholarly journals Vanishing of Massey Products and Brauer Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 730-740 ◽  
Author(s):  
Ido Efrat ◽  
Eliyahu Matzri
Keyword(s):  
Prime Number ◽  
Galois Cohomology ◽  
Brauer Groups ◽  
Central Simple Algebras ◽  
Massey Products ◽  
Global Fields ◽  
Root Of Unity ◽  
Simple Algebras ◽  
Central Simple

AbstractLet p be a prime number and F a field containing a root of unity of order p. We relate recent results on vanishing of triple Massey products in the mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Mináč, and Tân, to classical results in the theory of central simple algebras. We prove a stronger form of the vanishing property for global fields.

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