Totally Disconnected Groups and their Automorphism

虽然某些完全不连通的局部紧致拓扑群（如无限群、图的自同构群和局部域上的线性代数群）已经用特定的工具成功地研究了很长时间，但一般完全不连通群的结构理论是在20世纪90年代George a . Willis （Newcastle， N.S.W, Australia）发表了一篇开创性的论文后才发展起来的。目前的项目旨在促进G. A. Willis和申请人之间的进一步合作，并得到澳大利亚方面的资助。它的目标有两个：1。进一步发展了完全不连通群及其自同构的结构理论，特别是对与自同构相关的收缩群有了进一步的认识。利用一般结构理论的思想，将以前只知道的关于p进李群及其自同构的结果推广到局部正特征域上李群的情况。

While specific classes of totally disconnected, locally compact topological groups (like profinite groups, automorphism groups of graphs and linear algebraic groups over local fields) have been studied successfully for a long time with specific tools, a structure theory for general totally disconnected groups only developed in the 1990s after a seminal paper by George A. Willis (Newcastle, N.S.W., Australia). The current project intends to enable further cooperation between G. A. Willis and the applicant, complemented by funding from the Australian side. Its goals are twofold:1. To develop further the structure theory of totally disconnected groups and their automorphisms, notably to obtain further insight into the contraction groups associated with automorphisms.2. To extend results previously only known for p-adic Lie groups and their automorphisms to the case of Lie groups over local fields of positive characteristic, using ideas from the general structure theory.