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- Jean-Luc Chabert, Giulio Peruginelli
- 2015

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.

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)

- 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)

- Joseph H Silverman, Jackie Anderson, Rob Benedetto, John Cullinan, Xander Faber, Anthony Flatters +6 others
- 2008

Acknowledgements Page vi I would like to thank the following people for sending me comments and corrections:

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