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

Let Φ be an endomorphism of P1Q, 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)

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 Ẑ, the profinite completion of Z with respect to the fundamental system of neighbourhoods of 0 consisting of all non-zero ideals of Z.

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[X1, . . . , Xm] such that f(Z) = g(Z). We offer a necessary and sufficient condition on f for this to be possible. In particular it turns out that some power of 2 is a… (More)

Let V be a valuation domain of rank one and quotient field K. Let K̂ be a fixed algebraic closure of the v-adic completion K̂ of K and let V̂ be the integral closure of V̂ in K̂. 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 ∈ K̂ ∪ {∞}, namely, the valuation… (More)

- Irena Swanson, Craig Huneke, +14 authors Bernd Ulrich
- 2013

p. 8, lines 6–7 of proof of 1.3.3: replace “The lowest degree component” by “The lowest degree component monomial”; replace “components” by “component monomials”. p. 12, in Definition 1.4.7, now allow the Newton polyhedron to be the convex hull to be either in R or in Q. This harmonizes with the subsequent general definition of the Newton polyhedron in… (More)

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