Geodesic
Divisible subgroups of Brauer groups and trace forms of central simple algebras
Documenta mathematica, Tome 6 (2001), pp. 489-500.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $F$ be a field of characteristic different from 2 and assume that $F$ satisfies the strong approximation theorem on orderings ($F$ is a SAP field) and that $I^3(F)$ is torsion-free. We prove that the 2-primary component of the torsion subgroup of the Brauer group of $F$ is a divisible group and we prove a structure theorem on the 2-primary component of the Brauer group of $F$. This result generalizes well-known results for algebraic number fields. We apply these results to characterize the trace form of a central simple algebra over such a field in terms of its determinant and signatures.
Classification : 16K50, 11E81, 11E04
Keywords: central simple algebras, trace forms, Brauer groups 
@article{DOCMA_2001__6__a2,
     author = {Berhuy, Gr\'egory and Leep, David B.},
     title = {Divisible subgroups of {Brauer} groups and trace forms of central simple algebras},
     journal = {Documenta mathematica},
     pages = {489--500},
     publisher = {mathdoc},
     volume = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a2/}
}
TY  - JOUR
AU  - Berhuy, Grégory
AU  - Leep, David B.
TI  - Divisible subgroups of Brauer groups and trace forms of central simple algebras
JO  - Documenta mathematica
PY  - 2001
SP  - 489
EP  - 500
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a2/
LA  - en
ID  - DOCMA_2001__6__a2
ER  - 
%0 Journal Article
%A Berhuy, Grégory
%A Leep, David B.
%T Divisible subgroups of Brauer groups and trace forms of central simple algebras
%J Documenta mathematica
%D 2001
%P 489-500
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a2/
%G en
%F DOCMA_2001__6__a2
Berhuy, Grégory; Leep, David B. Divisible subgroups of Brauer groups and trace forms of central simple algebras. Documenta mathematica, Tome 6 (2001), pp. 489-500. http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a2/