  Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560)
Weil-\'etale cohomology $H^i_\text{W,c} (X, \mathbb{Z} (n))$ for a proper,
regular arithmetic scheme $X$ (i.e. separated and of finite type over
$\operatorname{Spec} \mathbb{Z}$) and $n \in \mathbb{Z}$. In the case when $n <
0$, we generalize their construction to an arbitrary arithmetic scheme $X$,
thus removing the proper and regular assumption. The construction assumes
finite generation of suitable \'etale motivic cohomology groups.
