Geodesic
Divisible subgroups of Brauer groups and trace forms of central simple algebras
Documenta mathematica, Tome 6 (2001), pp. 489-500
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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 I3(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.
DOI : 10.4171/dm/112
Classification : 11E04, 11E81, 16K50
Mots-clés : trace forms, central simple algebras, Brauer groups 
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     author = {Gr\'egory Berhuy and David B. Leep},
     title = {Divisible subgroups of {Brauer} groups and trace forms of central simple algebras},
     journal = {Documenta mathematica},
     pages = {489--500},
     year = {2001},
     volume = {6},
     doi = {10.4171/dm/112},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/112/}
}
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Grégory Berhuy; David B. Leep. Divisible subgroups of Brauer groups and trace forms of central simple algebras. Documenta mathematica, Tome 6 (2001), pp. 489-500. doi: 10.4171/dm/112

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