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arXiv · 2510.25931

Adelic Mordell-Lang and the Brauer-Manin obstruction

Brendan Creutz
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Abstract

Let $X$ be a closed subvariety of an abelian variety $A$ over a global function field $k$ such that the base change of $A$ to an algebraic closure does not have any positive dimensional isotrivial quotient. We prove that every adelic point on $X$ which is the limit of a sequence of $k$-rational points on $A$ is a limit of $k$-rational points on $X$. Assuming finiteness of the Tate-Shafarevich group of $A$, this implies that the rational points on $X$ are dense in the Brauer set of $X$. Similar results are obtained over totally imaginary number fields, conditionally on an adelic Mordell-Lang conjecture.

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Brendan Creutz. 2025-10-29. Adelic Mordell-Lang and the Brauer-Manin obstruction. https://arxiv.org/abs/2510.25931

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