The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi)

Details The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi) The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi)

2008-11-19

arxiv.org/abs/0811.3153v1

Mathematics

Algebraic Geometry

35 pages. This is the text of my Bourbaki talk in march 2008

Scientific paper

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.

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