arXiv subjects

F. Amoroso

Publications and source records attributed to F. Amoroso.

3 recordsLinked to original sources

arXiv2025

Sur une conjecture de Schinzel

We give a new proof of a conjecture of Schinzel on the intersection of a subvariety of codimension at least 2 in a power of the multiplicative group with a torus of dimension 1. The proof rests on a geometric B\'ezout's theorem of P. Philippon and on lower bounds for the height of the first author, S. David and E. Viada. It gives for the first time an explicit result, depending on the height and degree of the variety. It is inspired on a similar statement on products of elliptic curves, by S. Checcoli, F. Veneziano and E. Viada.

math.NT↗

arXiv2017

Bounded Height in Pencils of Finitely Generated Subgroups

We prove height bounds concerning intersections of finitely generated subgroups in a torus with algebraic subvarieties, all varying in a pencil. This vastly extends the previously treated constant case and involves entirely different, and more delicate, techniques.

math.NT↗

arXiv2015

Unlikely intersections and multiple roots of sparse polynomials

We present a structure theorem for the multiple non-cyclotomic irreducible factors appearing in the family of all univariate polynomials with a given set of coefficients and varying exponents. Roughly speaking, this result shows that the multiple non-cyclotomic irreducible factors of a sparse polynomial, are also sparse. To prove this, we give a variant of a theorem of Bombieri and Zannier on the intersection of a fixed subvariety of codimension 2 of the multiplicative group with all the torsion curves, with bounds having an explicit dependence on the height of the subvariety. We also use this latter result to give some evidence on a conjecture of Bolognesi and Pirola.

math.NT↗