Bright, Martin. (2011) Evaluating Azumaya algebras on cubic surfaces. Manuscripta Mathematica, Vol.134 (No.3-4). pp. 405-421. ISSN 0025-2611

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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) -> Q/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-Thelene, Kanevsky and Sansuc.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Manuscripta Mathematica
Publisher:	Springer
ISSN:	0025-2611
Date:	March 2011
Volume:	Vol.134
Number:	No.3-4
Page Range:	pp. 405-421
Identification Number:	10.1007/s00229-010-0400-2
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Heilbronn Institute for Mathematical Research
URI:	http://wrap.warwick.ac.uk/id/eprint/41544

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