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

Posted in
Günter Harder
Wed, 2017-06-14 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar
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 an L-function attached to 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.
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