Evidence for the Dynamical Brauer-Manin Criterion
Number Theory
2013-10-24 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1305.4398,
title = {Evidence for the Dynamical Brauer-Manin Criterion},
author = {Ekaterina Amerik and Par Kurlberg and Khoa Nguyen and Adam Towsley and Bianca Viray and Jose Felipe Voloch},
journal= {arXiv preprint arXiv:1305.4398},
year = {2013}
}