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Brauer groups of genus zero extensions of number fields

Author(s): Jack Sonn; John Swallow
Journal: Trans. Amer. Math. Soc. 357 (2005), 2723-2738.
MSC (2000): Primary 16K40, 12G05; Secondary 14H05
Posted: July 16, 2004
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Abstract: We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions $E$ of the rational numbers $\mathbb{Q} $ that are split by $\mathbb{Q} (\sqrt{2})$, $\operatorname{Br}(E)\cong \operatorname{Br}(\mathbb{Q} (t))$.

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Additional Information:

Jack Sonn
Affiliation: Department of Mathematics, Technion---Israel Institute of Technology, Haifa 32000 Israel
Email: sonn@math.technion.ac.il

John Swallow
Affiliation: Department of Mathematics, Davidson College, Box 7046, Davidson, North Carolina 28035-7046
Email: joswallow@davidson.edu

DOI: 10.1090/S0002-9947-04-03560-3
PII: S 0002-9947(04)03560-3
Received by editor(s): February 14, 2003
Received by editor(s) in revised form: September 23, 2003
Posted: July 16, 2004
Additional Notes: The first author's research was supported by the Fund for Promotion of Research at the Technion
The second author's research as supported in part by an International Research Fellowship, awarded by the National Science Foundation (INT--980199) and held at the Technion---Israel Institute of Technology during 1998--1999, and a Young Investigator Grant from the National Security Agency (MDA904-02-1-0061)
Copyright of article: Copyright 2004, American Mathematical Society

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