Rational points on Grassmannians and unlikely intersections in tori

Type: Article

Publication Date: 2016-01-22

Citations: 14

DOI: https://doi.org/10.1112/blms/bdv091

Abstract

In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in the multiplicative group of dimension n with algebraic subgroups of dimension n-2. 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".

Locations

  • Bulletin of the London Mathematical Society - View
  • arXiv (Cornell University) - View - PDF
  • edoc (University of Basel) - View - PDF
  • Oxford University Research Archive (ORA) (University of Oxford) - View - PDF
  • DataCite API - View

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