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 will report on 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.

Gasbarri, C. (2009). The strong abc conjecture over function fields [after McQuillan and Yamanoi]. ASTÉRISQUE(326), 219-256.

The strong abc conjecture over function fields [after McQuillan and Yamanoi]

GASBARRI, CARLO
2009-01-01

Abstract

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 will report on 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.
Pubblicato
Rilevanza internazionale
Articolo
Comitato scientifico
Settore MAT/03 - Geometria
English
Gasbarri, C. (2009). The strong abc conjecture over function fields [after McQuillan and Yamanoi]. ASTÉRISQUE(326), 219-256.
Gasbarri, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/121049
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