The Franke filtration is a finite filtration of the space of automorphic forms on a connected
reductive linear algebraic group defined over an algebraic number field. The main feature of …

This paper investigates the cohomology of SLn (Z), n≥ 2,“right outside” what one calls the
“stable range”. More precisely, a qualitative non-vanishing result for the cohomology Hq …

Abstract In his famous paper [11], J. Franke has defined a certain finite filtration of the space
of automorphic forms of a general reductive group, which captures most of its internal …

The cohomology of an arithmetic congruence subgroup of a connected reductive algebraic
group defined over a number field is captured in the automorphic cohomology of that group …

Let U/Q be a unitary group of Q-rank one so that the group of real points U (R)≅ U (n, 1). The
group U is only quasi-split over Q if and only if n= 1, 2. The cohomology of a congruence …

The present thesis provides a survey of results and techniques from the Langlands program
which allow for the computation of the ℓ-adic cohomology of local systems on Shimura …

During the past ten years of the most inspiring and very fruitful collaboration with Joachim
Schwermer, we have carefully studied the non-vanishing conditions for certain summands in …

We set up a general framework to compute the exact multiplicity with which certain
automorphic representations appear in both the cuspidal and Eisenstein cohomology of …

We prove an arithmeticity result for a class of cohomological residual automorphic
representations of a general reductive group $ G $. More precisely, we show that this class …

The purpose of this thesis is to construct nontrivial elements in the Bloch--Kato Selmer group
of the symmetric cube of the Galois representation attached to a cuspidal holomorphic …