Evaluating Azumaya algebras on cubic surfaces
Number Theory
2011-01-27 v4 Algebraic Geometry
Abstract
Let X be a cubic surface over a local number 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. We show that a suitably generic cubic surface over a number field, whose reduction at some prime is a cone, has no Brauer-Manin obstruction. This extends results of Colliot-Th\'el\`ene, Kanevsky and Sansuc.
Cite
@article{arxiv.0810.3535,
title = {Evaluating Azumaya algebras on cubic surfaces},
author = {Martin Bright},
journal= {arXiv preprint arXiv:0810.3535},
year = {2011}
}
Comments
14 pages; minor changes