On the properness of the moduli space of stable surfaces over $\mathbb{Z}[1/30]$

Abstract

We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional log canonical singularities at closed point of characteristic $p\ne 2,3$ and $5$ which are not log canonical centres.

33 pages, minor modifications. To appear in Moduli

Cited by in corpus (1)

• Families of stable 3-folds in positive characteristic