Rational points on Grassmannians and unlikely intersections in tori

Author: 

Capuano, L
Masser, D
Pila, J
Zannier, U

Publication Date: 

February 2016

Journal: 

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY

Last Updated: 

2019-04-27T21:14:47.357+01:00

Issue: 

1

Volume: 

48

DOI: 

10.1112/blms/bdv091

page: 

141-154

abstract: 

© 2016 London Mathematical Society. In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in Gmn with algebraic subgroups of dimension n-2. Actually, the present conclusion will give more uniform bounds with 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'.

Symplectic id: 

572460

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article