Brauer groups of genus zero extensions of number fields
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- by Jack Sonn and John Swallow PDF
- Trans. Amer. Math. Soc. 357 (2005), 2723-2738 Request permission
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 $\mathbb {Q}(\sqrt {2})$, $\operatorname {Br}(E)\cong \operatorname {Br}(\mathbb {Q}(t))$.References
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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
- Received by editor(s): February 14, 2003
- Received by editor(s) in revised form: September 23, 2003
- Published electronically: 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 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 2723-2738
- MSC (2000): Primary 16K40, 12G05; Secondary 14H05
- DOI: https://doi.org/10.1090/S0002-9947-04-03560-3
- MathSciNet review: 2139524