Totally Disconnected Groups and their Automorphism

虽然一些特殊的完全不连通的局部紧拓扑群(如局部域上的普适群、图的自同构群和线性代数群)已经用特定的工具成功地研究了很长一段时间，但一般的完全不连通群的结构理论直到20世纪90年代才在George A.Willis(澳大利亚纽卡斯尔)的一篇开创性论文之后得到了发展。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金补充。它的目的有两个：1.进一步发展完全不连通群及其自同构的结构理论，特别是进一步深入了解与自同构相关的压缩群。利用一般结构理论的思想，将以前已知的仅关于p-进Lie群及其自同构的结果推广到具有正特征的局部域上的Lie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.