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Working paper

Evidence for the Dynamical Brauer-Manin Criterion

arxiv.org. math. Cornell University, 2013. No. 1305.4398.
Amerik E., Kurlberg P., Nguyen K., Towsley A., Viray B., Voloch J. F.
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.