The Hilbert Stack
Algebraic Geometry
2015-03-17 v2
Abstract
Let \pi : X -> S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack, the Hilbert stack, parameterizing proper algebraic stacks mapping quasi-finitely to X. This was previously unknown, even for a morphism of schemes.
Cite
@article{arxiv.1011.5484,
title = {The Hilbert Stack},
author = {Jack Hall and David Rydh},
journal= {arXiv preprint arXiv:1011.5484},
year = {2015}
}
Comments
29 pages; major revision; no longer uses derived algebraic geometry; introduced Generalized Stein factorization; greatly simplified d\'evissage argument; two new appendices on coherent cohomology on formal schemes and henselian pairs