Coadmissible modules over Fréchet-Stein algebras

Let K be a non-archimedean field of mixed characteristic (0,p), and let L be a finite extension of
the p-adic numbers contained in K. The speaker is interested in the continuous representations of a
given L-analytic group G in locally convex (usually infinite dimensional) topological vector spaces over K.
This is, up to technicalities, equivalent to studying certain topological modules over the locally
analytic distribution algebra D(G,K) of G. But doing algebra with topological objects is hard!
In this talk, we present an excellent remedy, found by Schneider and Teitelbaum in the early 2000s.