Existence of coarse moduli superspaces for Deligne--Mumford superstacks

Abstract

We prove that every Deligne--Mumford superstack over $\mathbb{Z}[1/2]$ 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.

arXiv comment32 pages, comments welcome!