论文标题
分析性斧头链苯甲油定理，用于半阿您品种和内凡林纳理论
Analytic Ax-Schanuel Theorem for semi-abelian varieties and Nevanlinna theory
论文作者
论文摘要
本文的目的是探索整个曲线的nevanlinna理论$ \ exh_a f：=（\ exp_af，f）：\ c \ to a \ times \ lie（a）$（a）$与整个曲线$ f：\ c \ to \ c \ to \ to \ lie（a）$（a）$，其中$ \ exp_a：\ exp_a：\ lie（whene $ \ exp_a：\ lie（a）首先，我们将Nevanlinna理论证明提供给半阿伯式品种的{\ Emantialt ax-schanuel定理}，这是J. AX 1972在正式的功率序列（Ax-Schanuel定理）的情况下证明的。我们假设$ f $的某些非降低条件，以使矢量值函数$ f（z）-f（z）-f（0）\ in \ lie（a）\ iso \ c^n $是$ \ q $ - 在$ a =（\ c^*）^n $的情况下，$ \ q $ - q $ linarearly独立。然后，通过使用log bloch-ochiai定理和我们显示的关键估计，我们证明了$ \ td_ \ c \，\ exh_a f \ geq n+ 1 $。 我们的下一个目标是为$ \ exh_a f $及其$ k $ -JET升降机建立一个{\ em 2nd Main Theorem}，并在第一级上具有截断的计数功能。
The purpose of this paper is to explore Nevanlinna theory of the entire curve $\exh_A f:=(\exp_Af,f):\C \to A \times \Lie(A)$ associated with an entire curve $f: \C \to \Lie(A)$, where $\exp_A:\Lie(A)\to A$ is an exponential map of a semi-abelian variety $A$. Firstly we give a Nevanlinna theoretic proof to the {\em analytic Ax-Schanuel Theorem} for semi-abelian varieties, which was proved by J. Ax 1972 in the case of formal power series (Ax-Schanuel Theorem). We assume some non-degeneracy condition for $f$ such that the elements of the vector-valued function $f(z)-f(0) \in \Lie(A)\iso \C^n$ are $\Q$-linearly independent in the case of $A=(\C^*)^n$. Then by making use of the Log Bloch-Ochiai Theorem and a key estimate which we show, we prove that $\td_\C\, \exh_A f \geq n+ 1$. Our next aim is to establish a {\em 2nd Main Theorem} for $\exh_A f$ and its $k$-jet lifts with truncated counting functions at level one.
