Evaluating Azumaya algebras on cubic surfaces
arXiv:0810.3535 · doi:10.1007/s00229-010-0400-2
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-Thélène, Kanevsky and Sansuc.
arXiv comment14 pages; minor changes