The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi)
Abstract
Description
The $abc$ conjecture predicts a highly non trivial upper bound for the height of an algebraic point in terms of its discriminant and its intersection with a fixed divisor of the projective line counted without multiplicity. We describe the two independent proofs of the strong $abc$ conjecture over function fields given by McQuillan and Yamanoi. The first proof relies on tools from differential and algebraic geometry; the second relies on analytic and topological methods. They correspond respectively to the Nevanlinna and the Ahlfors approach to the Nevanlinna Second Main Theorem.
35 pages. This is the text of my Bourbaki talk in march 2008
35 pages. This is the text of my Bourbaki talk in march 2008