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arXiv · 1711.01541

No transcendental Brauer-Manin obstructions on abelian varieties

Brendan Creutz
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Abstract

Suppose $X$ is a torsor under an abelian variety $A$ over a number field. We show that any adelic point of $X$ that is orthogonal to the algebraic Brauer group of $X$ is orthogonal to the whole Brauer group of $X$. We also show that if there is a Brauer-Manin obstruction to the existence of rational points on $X$, then there is already an obstruction coming from the locally constant Brauer classes. These results had previously been established under the assumption that $A$ has finite Tate-Shafarevich group. Our results are unconditional.

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Brendan Creutz. 2017-11-05. No transcendental Brauer-Manin obstructions on abelian varieties. https://arxiv.org/abs/1711.01541

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