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

Emelie Arvidsson; Fabio Bernasconi; Zsolt Patakfalvi

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arXiv · 2302.05651

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

Emelie Arvidsson·Fabio Bernasconi·Zsolt Patakfalvi

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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 $p \neq 2, 3$ and $5$ which are not log canonical centres.

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Emelie Arvidsson, Fabio Bernasconi, Zsolt Patakfalvi. 2023-02-11. On the properness of the moduli space of stable surfaces over $\mathbb{Z}[1/30]$. https://arxiv.org/abs/2302.05651

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