### A non-selfdual 4-dimensional Galois representation, by Jasper Scholten

In this paper it is explained how one can construct
non-selfdual 4-dimensional
$\ell$-adic Galois representations of Hodge type
$h^{3,0}=h^{2,1}=h^{1,2}=h^{0,3}=1$,
assuming a hypothesis concerning the cohomology
of a certain threefold.
For one such a representation the first 80000 coefficients of its
$L$-function are computed, and it is numerically verified that this
$L$-function satisfies a functional equation. Also a candidate for
the conductor is obtained.

Jasper Scholten <jasper@math.rug.nl>