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On Vojta's 1+epsilon Conjecture(论Vojta 1+epsilon 猜想)
Chen Xi 教授(University of Alberta)
2018-01-01 12:13  华东师范大学

曹锡华代数论坛
报告人:Chen Xi 教授(University of Alberta)
时间:2010年12月28日(周二)下午15:00-16:00
地点:闵行校区数学楼102报告厅

On Vojta's 1+epsilon Conjecture
(中文标题:论Vojta 1+epsilon 猜想)

Abstract
In his famous lecture notes book, Paul Vojta formulated a series of conjectures in arithmetic geometry. One of them is so-called 1+epsilon conjecture, which gives a bound on the height of a rational point on a curve in terms of its discriminant. Vojta proved a weakened functional version of the conjecture with 1 replaced by 2. A full proof for the functional version was eventually given by K. Yamanoi using value distribution theory in 2004. Following an approach suggested by M. McQuillan, I've given an alternative algebro-geometric proof recently. I'll talk about the background of this conjecture and also a sketch of my proof.