The linear and quadratic Schur subgroups over the -integers of a number field

Author:
Carl R. Riehm

Journal:
Proc. Amer. Math. Soc. **107** (1989), 83-87

MSC:
Primary 11R65; Secondary 11R54, 13A20, 20C10

DOI:
https://doi.org/10.1090/S0002-9939-1989-0979218-0

MathSciNet review:
979218

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Abstract: Let be an algebraic number field and let be a ring of -integers in (where is a set of primes of containing all the archimedean primes); that is to say, is a Dedekind domain whose field of quotients is . In analogy with a theorem of T. Yamada in the case of a field of characteristic 0, it is shown that if is the Schur subgroup of the Brauer group and if , where is any field containing the maximal abelian extension of in , then , i.e. the Brauer classes in are those obtained from by extension of the scalars to . A similar theorem is proved as well in the case of the Schur subgroup of the quadratic Brauer group , where is an involution of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0979218-0

Keywords:
Schur subgroup,
integral Brauer group,
integral representations,
representations of finite groups,
quadratic Brauer group,
Azumaya algebras,
algebraic number fields

Article copyright:
© Copyright 1989
American Mathematical Society