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Evaluating Azumaya algebras on cubic surfaces
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Bright, M. (Martin) (2011) Evaluating Azumaya algebras on cubic surfaces. Manuscripta Mathematica, Volume 134 (Number 3-4). pp. 405-421. doi:10.1007/s00229-010-0400-2 ISSN 0025-2611.
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Official URL: http://dx.doi.org/10.1007/s00229-010-0400-2
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Azumaya algebras, Surfaces, Cubic | ||||
Journal or Publication Title: | Manuscripta Mathematica | ||||
Publisher: | Springer | ||||
ISSN: | 0025-2611 | ||||
Official Date: | March 2011 | ||||
Dates: |
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Volume: | Volume 134 | ||||
Number: | Number 3-4 | ||||
Page Range: | pp. 405-421 | ||||
DOI: | 10.1007/s00229-010-0400-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | University of Bristol. Heilbronn Institute for Mathematical Research |
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