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We show that every polynomial overring of the ring Int(Z) of polynomials which are integer-valued over Z may be considered as the ring of polynomials which are integer-valued over some subset of Z, the profinite completion of Z with respect to the fundamental system of neighbourhoods of 0 consisting of all non-zero ideals of Z.

- Jung Kyu Canci, Giulio Peruginelli, Dajano Tossici
- 2012

Let Φ be an endomorphism of P 1 Q , the projective line over the algebraic closure of Q, of degree ≥ 2 defined over a number field K. Let v be a non-archimedean valuation of K. We say that Φ has critically good reduction at v if any pair of distinct ramification points of Φ do not collide under reduction modulo v and the same holds for any pair of branch… (More)

- G. Peruginelli, U. Zannier
- 2013

Given a polynomial f ∈ Q[X] such that f (Z) ⊂ Z, we investigate whether the set f (Z) can be parametrized by a multivariate polynomial with integer coefficients, that is, the existence of g ∈ Z[X 1 ,. .. , X m ] such that f (Z) = g(Z m). We offer a necessary and sufficient condition on f for this to be possible. In particular it turns out that some power of… (More)

Let V be a valuation domain of rank one and quotient field K. Let K be a fixed algebraic closure of the v-adic completion K of K and let V be the integral closure of V in K. We describe a relevant class of valuation domains W of the field of rational functions K(X) which lie over V , which are indexed by the elements α ∈ K ∪ {∞}, namely, the valuation… (More)

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