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 locallystable reduction conjecture for stable surfaces. This relies on a local KawamataViehweg vanishing theorem for for 3dimensional log canonical singularities at closed point of characteristic $p \neq 2, 3$ and $5$ which are not log canonical centres.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.05651
 arXiv:
 arXiv:2302.05651
 Bibcode:
 2023arXiv230205651A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 33 pages, minor modifications. To appear in Moduli