Existence of coarse moduli superspaces for Deligne--Mumford superstacks

We prove that every Deligne–Mumford superstack over $\mathbb{Z}[1\mathrm{/}2]$ with finite inertia admits a coarse moduli superspace. This generalizes the Keel–Mori theorem to the super setting. As part of our argument, we introduce a notion of integral morphisms in algebraic supergeometry and use it to establish an effective descent result for étale morphisms of algebraic superspaces. We also include an example of a non-Deligne–Mumford superstack with finite inertia that does not admit a coarse moduli superspace.