本项目主要研究对象是Pi-可除O-模。项目研究包括Pi-可除O-模的分类，定义于特征p的域上的Pi-可除O-模的结构，以及Pi-可除O-模的形变理论。利用display理论，我们对Pi-可除O-模有一个完整地分类。当基底为特征p的完备域时域，我们可以容易得到Dieudonne理论的推广，从而能够对Pi-可除O-模的结构作深入的精细的研究。我们的具体研究问题包括Pi-可除O-模的slope filtration的存在性，关于Newton polygon的purity结果，极小的Pi-可除O-模，Traverso的同源猜想，以及Pi-可除O-模的形变理论。这些基础问题的解决将提升我们对Pi-可除O-模本身的理解，也有利于我们将Pi-可除O-模联系到代数数论和代数几何的相关问题上，得到新的进展。

The proposed project focuses on the study of Pi-divisible O-modules. The research topics include the classification of Pi-divisible O-modules, the structure of Pi-divisible O-modules over fields of characteristic p, and deformations of Pi-divisible O-modules. Using display theory, we obtain a complete classification of Pi-divisible O-modules in a very general setting. In particular, if the base is a perfect field of characteristic p, we may easily generalize Dieudonne theory, hence may study Pi-divisible O-modules in a more explicit way. More precisely, we study the following problems: the existence of slope filtration of Pi-divisible O-modules, the purity result about the Newton polygon of Pi-divisible O-modules, minimal Pi-divisible O-modules, Traverso's isogeny conjecture, and deformations of Pi-divisible O-modules. Solving these problems would help us to understand Pi-divisible O-modules and connect them with related research topics in algebraic number theory and algebraic geometry.