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arXiv · 1305.4398

Evidence for the Dynamical Brauer-Manin Criterion

Ekaterina Amerik·Par Kurlberg·Khoa Nguyen·Adam Towsley·Bianca Viray·Jose Felipe Voloch
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Abstract

Let f:X->X be a morphism of a variety over a number field K. We consider local conditions and a "Bruaer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P in X(K) to be disjoint from a subvariety V of X, i.e., the intersection of the orbit of P with V is empty. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection of the orbit of P with V; this evidence stems from a probabilistic argument as well as unconditional results in the case of etale maps.

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Ekaterina Amerik, Par Kurlberg, Khoa Nguyen, Adam Towsley, Bianca Viray, Jose Felipe Voloch. 2013-10-23. Evidence for the Dynamical Brauer-Manin Criterion. https://arxiv.org/abs/1305.4398

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