Taking place at Université Pierre et Marie Curie, 8th of June, 2017.

Günter Harder (Hausdorff Center for Mathematics, Bonn)

## Divisibility of *L*-values and the existence of non trivial cohomology classes

We consider a very special class of congruence subgroups of Sl_2(**Z**[i]) ;
for each of these congruence subgroups, the Eisenstein cohomology is essentially
described in terms of special values of a specific Hecke character (which is determined by the subgroup).

We analyze these special values and show that the divisibility of these special values
by certain primes ℓ implies that the cohomology of the congruence subgroup
contains some non trivial classes. These classes are either cuspidal classes or they
are ℓ-torsion classes.

In an experiment always the second case occurs (computation by D. Yasaki).

Back to the colloquium on the Geometry of Groups and Numbers