Abstract
In the context that arose from an old problem of Lang regarding the torsion points on subvarieties of Gmd, we describe the points that lie in a given variety, are defined over the cyclotomic closure kc of a number field k, and map to a torsion point under a finite projection to Gmd. We apply this result to obtain a sharp and explicit version of Hilbert's irreducibility theorem over kc. Concerning the arithmetic of dynamics in one variable, we obtain by related methods a complete description of the polynomials having an infinite invariant set contained in kc. In particular, we answer a number of long-standing open problems posed by W. Narkiewicz and which he eventually collected explicitly in the book [N2]
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