Specialization morphisms
Ildar Gaisin, John Welliaveetil

TL;DR
This paper introduces specialization morphisms from locally noetherian analytic adic spaces to schemes, establishing their properties and applications, including properness and compatibility of nearby cycles functor.
Contribution
It defines a new notion of specialization morphisms in the adic space context, extending classical concepts and proving their properness and compatibility with nearby cycles.
Findings
Specialization morphisms are well-behaved and proper.
The classical specialization morphism is a special case.
Nearby cycles functor commutes with lower shriek in general.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation
