论文标题
相对半阿伯式品种的分析和理性部分
Analytic and rational sections of relative semi-abelian varieties
论文作者
论文摘要
亚洲品种中亚群的双波利度陈述和反曲面的补充允许算术类似物，这是由于疲惫的（和半亚伯利亚案例的vojta）。在Atti Accad中。纳兹。 Lincei Rend。 Lincei Mat。应用。 29（2018）由第二作者，分析和算术理论之间的类比也显示在证明级别上，即在雷诺定理（Manin-Mummford猜想）的证明中。本文的第一个目的是扩展到相对设置上述双曲线结果。我们将关注仿射代数曲线相对（半）阿贝尔方案的分析部分。 这些部分形成了一个组；尽管已经广泛研究了一组理性部分（Mordell-Weil组），但迄今为止，对分析部分的研究很少进行。我们借此机会通过Nevanlinna理论来开发这种显然是新理论的基本结构，从而定义了分析部分的高度或顺序函数概念。
The hyperbolicity statements for subvarieties and complements of hypersurfaces in abelian varieties admit arithmetic analogues, due to Faltings (and Vojta for the semi-abelian case). In Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018) by the second author, an analogy between the analytic and arithmetic theories was shown to hold also at proof level, namely in a proof of Raynaud's theorem (Manin-Mumford Conjecture). The first aim of this paper is to extend to the relative setting the above mentioned hyperbolicity results. We shall be concerned with analytic sections of a relative (semi-)abelian scheme over an affine algebraic curve. These sections form a group; while the group of rational sections (the Mordell-Weil group) has been widely studied, little investigation has been pursued so far on the group of the analytic sections. We take the opportunity of developing some basic structure of this apparently new theory, defining a notion of height or order functions for the analytic sections, by means of Nevanlinna theory.
