Rational points on Grassmannians and unlikely intersections in tori

Capuano, Laura and Masser, David and Pila, Jonathan and Zannier, Umberto. (2016) Rational points on Grassmannians and unlikely intersections in tori.

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Official URL: https://edoc.unibas.ch/69969/

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In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in $\mathbb{G}_m^n$ with algebraic subgroups of dimension $n−2$. Actually, the present conclusion will give more uniform bounds which respect to the former statement. The proof uses a method introduced for the first time by Pila and Zannier to give an alternative proof of Manin-Mumford conjecture and a theorem to count points that satisfy a certain number of linear conditions with rational coefficients. This method has been largely used in many different problems in the context of “unlikely intersections”.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Masser, David
Item Type:Preprint
Publisher:Universität Basel
Last Modified:21 Apr 2019 11:53
Deposited On:28 Mar 2019 09:51

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