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Rational distances from given rational points in the plane
Pietro Corvaja, Amos Turchet, Umberto Zannier
In this paper we study sets of points in the plane with rational distances from r prescribed points P_1, ...,P_r. A crucial case arises for r = 3, where we provide simple necessary…
Greatest Common Divisor results on semiabelian varieties and a Conjecture of Silverman
Fabrizio Barroero, Laura Capuano, Amos Turchet
A divisibility sequence is a sequence of integers such that divides if divides . Results of Bugeaud, Corvaja, Zannier, among others, have shown that th…
Divisibility of polynomials and degeneracy of integral points
Erwan Rousseau, Julie Tzu-Yueh Wang, Amos Turchet
We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties t…
Around the Chevalley-Weil Theorem
Pietro Corvaja, Amos Turchet, Umberto Zannier
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological t…
The Erdős-Ulam problem, Lang's conjecture, and uniformity
Kenneth Ascher, Lucas Braune, Amos Turchet
A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's Conjecture, that the cardinalities of…