The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi)
| dc.creator | Gasbarri, Carlo | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:19:31Z | |
| dc.date.available | 2026-07-07T10:19:31Z | |
| dc.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. | |
| dc.description | 35 pages. This is the text of my Bourbaki talk in march 2008 | |
| dc.identifier | https://arxiv.org/abs/0811.3153 | |
| dc.identifier | http://arxiv.org/abs/0811.3153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174537 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G25, 11J97 | |
| dc.title | The strong $ABC$ conjecture over function fields (after McQuillan and Yamanoi) | |
| dc.type | text |