Evidence for the Dynamical Brauer–Manin Criterion

Let ϕ: X → X be a morphism of a variety over a number field K. We consider local conditions and a “Brauer–Manin” condition, defined by Hsia and Silverman, for the orbit of a point P ∈ X(K) to be disjoint from a subvariety V⊆X, i.e., for We provide evidence that the dynamical Brauer–Manin condition is sufficient to explain the lack of points in the intersection ; this evidence stems from a probabilistic argument as well as unconditional results in the case of étale maps.

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