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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The index of a Brauer class on a Brauer-Severi variety


Authors: Aidan Schofield and Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 333 (1992), 729-739
MSC: Primary 12E15; Secondary 14M99, 16E20, 16K40
MathSciNet review: 1061778
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Abstract: Let $ D$ and $ E$ be central division algebras over $ k$; let $ K$ be the generic splitting field of $ E$; we show that the index of $ D{ \otimes _k}K$ is the minimum of the indices of $ D \otimes {E^{ \otimes i}}$ as $ i$ varies. We use this to calculate the index of $ D$ under related central extensions and to construct division algebras with special properties.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1061778-X
PII: S 0002-9947(1992)1061778-X
Article copyright: © Copyright 1992 American Mathematical Society