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 Oϕ(P) ∩ V = ∅. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection Oϕ(P) ∩ V ; this evidence stems from a probabilistic argument as well as unconditional results in the case of ´etale maps.

• Type: Journal
• Year: 2016
• Where: EM
• Authors: Ekaterina Amerik, Pär Kurlberg, Khoa D. Nguyen, Adam Towsley, Bianca Viray, José Felipe Voloch
• Keywords: EM 2016, Management