Details:
Title  The residual Eisenstein cohomology of $mathrmSp_4$ over a totally real number field.  Author(s)  Neven Grbac, Harald Grobner  Type  Article in Journal  Abstract  Let
G
=
Sp
4
/k
be the
k
split symplectic group of
k
rank 2, where
k
is a totally real number field. In this paper we compute the Eisenstein co
homology of
G
with respect to any finite–dimensional, irreducible,
k
rational
representation
E
of
G
∞
=
R
k/
Q
G
(
R
), where
R
k/
Q
denotes the restriction of
scalars from
k
to
Q
. This approach is based on the work of Schwermer regard
ing the Eisenstein cohomology for
Sp
4
/
Q
, Kim’s description of the residual
spectrum of
Sp
4
, and the Franke filtration of the space of automorphic forms.
In fact, taking the representation theo
retic point of view, we write, for the
group
G
, the Franke filtration with respect to the cuspidal support, and give
a precise description of the filtration quotients in terms of induced representa
tions. This is then used as a prerequis
ite for the explicit computation of the
Eisenstein cohomology. The special focus is on the residual Eisenstein coho
mology. Under a certain compatibility c
ondition for the coefficient system
E
and the cuspidal support, we prove the existence of non–trivial residual Eisen
stein cohomology classes, which are not square–integrable, that is, represented
by a non–square–integrable residue of an Eisenstein serie
 ISSN  00029947; 10886850/e 
File 
 URL 
http://www.ams.org/journals/tran/201336510/S000299472013057960/home.html 
Language  English  Journal  Trans. Am. Math. Soc.  Volume  365  Number  10  Pages  51995235  Publisher  American Mathematical Society (AMS), Providence, RI  Year  2013  Edition  0  Translation 
No  Refereed 
No 
