Generalizations of Siegel's and Picard's theorems

• 成果类型: Article
• 署名作者: Levin, Aaron
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.609
• 发表日期: 2009
• 页码: 609-655
• 关键词: integral points; holomorphic-curves; complement

摘要

We prove new theorems that are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from C to affine curves. These include results on integral points over varying number fields of bounded degree and results on Kobayashi hyperbolicity. We give a number of new conjectures describing, from our point of view, how we expect Siegel's and Picard's theorems to optimally generalize to higher dimensions.