Specialization morphisms
Algebraic Geometry
2021-03-30 v1
Abstract
We define the notion of a specialization morphism from a locally noetherian analytic adic space to a scheme. This captures the (classical) specialization morphism associated to a formal scheme. There is a well behaved theory of compactifications and it turns out that the classical specialization morphism is \emph{proper} in this setup. As an application, we show that the nearby cycles functor commutes with lower shriek in great generality.
Cite
@article{arxiv.2103.14828,
title = {Specialization morphisms},
author = {Ildar Gaisin and John Welliaveetil},
journal= {arXiv preprint arXiv:2103.14828},
year = {2021}
}