Gluing for stable families of surfaces in mixed characteristic

Abstract

We study the normalizations of non-normal stable families of slc surfaces over an excellent DVR. In mixed characteristic, we establish a gluing statement that is relevant for the properness of the moduli space of such surfaces. We also study the fibers of such glued families, in mixed and equi-characteristic, and provide an essential result for slc adjunction in residue characteristic >5.

arXiv comment25 pages. Comments welcome at anytime. (v4: Final version, to appear in Algebraic Geometry. Abstract has been changed, minor corrections.)