Helge Glockner
Published 2008-04-14, updated 2015-01-06Version 4
These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes is to provide an introduction to p-adic Lie groups and Lie groups over fields of formal Laurent series, with an emphasis on relations to the structure theory of totally disconnected, locally compact groups. In particular, they contain a discussion of the scale, tidy subgroups and contraction groups for automorphisms of Lie groups over local fields. Special attention is paid to the case of Lie groups over local fields of positive characteristic.
Comments: v4: 29 pages, stronger focus on analytic Lie groups, update of references, open problems removed
Smooth Lie groups over local fields of positive characteristic need not be analytic
Locally compact groups built up from p-adic Lie groups, for p in a given set of primes
Chabauty limits of groups of involutions in $SL(2,F)$ for local fields
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