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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Embedding Galois problems and reduced norms
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by Teresa Crespo PDF
Proc. Amer. Math. Soc. 112 (1991), 637-639 Request permission

Abstract:

For certain embedding problems $\tilde G \to G \simeq {\text {Gal}}\left ( {L\left | K \right .} \right )$ associated to a representation $t:G \to {\text {Aut}}A$ of the group $G$ by automorphisms of a central simple $K$-algebra $A$ of dimension ${n^2}$, we prove that the solutions are the fields $L\left ( {{{\left ( {rN\left ( z \right )} \right )}^{1/n}}} \right )$, with $r$ running over ${K^ * }/{K^{ * n}}$ and $N\left ( z \right )$ the reduced norm of an invertible element $z$ in the algebra $B \otimes L$, for $B$ the twisted algebra of $A$ by $t$.
References
  • Teresa Crespo, Explicit solutions to embedding problems associated to orthogonal Galois representations, J. Reine Angew. Math. 409 (1990), 180–189. MR 1061524, DOI 10.1515/crll.1990.409.180
  • A. Fröhlich, Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants, J. Reine Angew. Math. 360 (1985), 84–123. MR 799658, DOI 10.1515/crll.1985.360.84
  • Serge Lang, Rapport sur la cohomologie des groupes, W. A. Benjamin, Inc., New York-Amsterdam, 1967 (French). MR 0212073
  • C. Soulé, ${K_2}$ et le groupe de Brauer, Séminaire Bourbaki, vol. 601, 1982/83.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 637-639
  • MSC: Primary 11E88; Secondary 12F10
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1057951-1
  • MathSciNet review: 1057951