Singular curves and the etale Brauer-Manin obstruction for surfaces
Algebraic Geometry
2013-11-25 v2 Number Theory
Abstract
We construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also construct a surface with a unique rational point and the infinite etale Brauer-Manin set. The key new ingredient is the arithmetic of singular projective curves.
Keywords
Cite
@article{arxiv.1212.6019,
title = {Singular curves and the etale Brauer-Manin obstruction for surfaces},
author = {Yonatan Harpaz and Alexei Skorobogatov},
journal= {arXiv preprint arXiv:1212.6019},
year = {2013}
}
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17 pages