English

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.

Keywords

Cite

@article{arxiv.2103.14828,
  title  = {Specialization morphisms},
  author = {Ildar Gaisin and John Welliaveetil},
  journal= {arXiv preprint arXiv:2103.14828},
  year   = {2021}
}
R2 v1 2026-06-24T00:36:28.048Z