Mathematics – Number Theory
Scientific paper
2008-10-20
Manuscripta Math., 134(3), 2011, pp. 405--421
Mathematics
Number Theory
14 pages; minor changes
Scientific paper
10.1007/s00229-010-0400-2
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.
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