BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
© 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'.
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