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

Schofield, Aidan; Van den Bergh, Michel

doi:10.1090/S0002-9947-1992-1061778-X

The index of a Brauer class on a Brauer-Severi variety
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by Aidan Schofield and Michel Van den Bergh PDF

Trans. Amer. Math. Soc. 333 (1992), 729-739 Request permission

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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