The main subject of this habilitation thesis are automorphic L-invariants.
Given an automorphic representation π of a semi-simple group G that fulfils several conditions - most notably that the local component of π at p is Steinberg - the automorphic L-invariants of π are p-adic numbers that are constructed from the π -isotypic component of the cohomology of p-arithmetic subgroups of G.
They conjecturally describe fine properties of the (local) p-adic Galois representation attached to π.