  We consider $\Sigma$-invariants of Artin groups that satisfy the
$K(\pi,1)$-conjecture. These invariants determine the cohomological finiteness
conditions of subgroups that contain the derived subgroup. We extend a known
result for even Artin groups of FC-type, giving a sufficient condition for a
character $\chi:A_\Gamma\to\mathbb{R}$ to belong to
$\Sigma^n(A_\Gamma,\mathbb{Z})$. We also prove some partial converses. As
applications, we prove that the $\Sigma^1$-conjecture holds true when there is
a prime $p$ that divides $l(e)/2$ for any edge with even label $l(e)>2$, we
generalize to Artin groups the homological version of Bestvina-Brady theorem
and we compute the $\Sigma$-invariants of all irreducible spherical and affine
Artin groups and triangle Artin groups, which provide a complete classification
of the $F_n$ and $FP_n$ properties of their derived subgroup.
