Evaluating Azumaya algebras on cubic surfaces
Identifieur interne : 000431 ( Main/Exploration ); précédent : 000430; suivant : 000432Evaluating Azumaya algebras on cubic surfaces
Auteurs : Martin Bright [Royaume-Uni]Source :
- Manuscripta Mathematica [ 0025-2611 ] ; 2011-03-01.
Abstract
Abstract: Let X be a cubic surface over a p-adic field k. Given an Azumaya algebra on X, we describe the local evaluation map $${X(k) \to \mathbb{Q}/\mathbb{Z}}$$ in two cases, showing a sharp dependence on the geometry of the reduction of X. When X has good reduction, then the evaluation map is constant. When the reduction of X is a cone over a smooth cubic curve, then generically the evaluation map takes as many values as possible. We show that such a cubic surface defined over a number field has no Brauer–Manin obstruction. This extends results of Colliot-Thélène, Kanevsky and Sansuc.
Url:
DOI: 10.1007/s00229-010-0400-2
Affiliations:
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