在正特征函数域上的超越性研究中，与Drinfeld模的算术和几何结构有关的典型函数的函数超越性以及在特殊点处的值的超越性一直都是人们关心的中心问题之一。近几年来，人们在这一方面取得了重大进展，但遗留的问题还有许多，其困难在于该领域目前常用的四个方法各自均有缺陷。为此我们需借助源自代数数论、算术代数几何以及代数群等方面的外来工具，一方面促进现有方法的融合，另一方面则是要实现方法上的突破，以便能更好地理解一般正特征函数域的算术与几何结构，并最终导致若干重要问题的解决，而这正是本项目研究的终极目标。

In the study of transcendence over function fields with positive characteristic, the transcendence of typical functions related to the arithmetic and geometric structures of Drinfeld modules and the transcendence of special values of these functions are always among the central problems considered by many authors. In recent years, important progresses have been made on this subject, but there are still many problems remained open, the difficulty consists in that each of the four methods applied currently in the domain has its proper defects. Hence we need borrow outer tools from algebraic number theory, arithmetic algebraic geometry, algebraic groups etc, on the one hand to promote the fusion of current methods, and on the other hand to realize a breakthrough in methods, so that we can understand better the arithmetic and geometric structures of general function fields with positive characteristic, and finally may be led to the solution of some important problems, and this is precisely the ultimate goal of the present proposal.