Weil restriction of p-adic analytic spaces

TL;DR

This paper investigates the Weil restriction functor within p-adic analytic spaces, establishing criteria for its representability and demonstrating its applications to the behavior of adic Néron models under tamely ramified base change.

Contribution

It provides the first criteria for the representability of Weil restriction functors in adic and Berkovich spaces, linking these to the behavior of Néron models in p-adic geometry.

Findings

Criteria for Weil restriction representability in adic and Berkovich spaces

Application to the good behavior of adic Néron models under tamely ramified base change

Enhanced understanding of functorial properties in p-adic analytic geometry

Abstract

We study the functor of Weil restriction in the category of Huber's adic spaces and in the category of Berkovich spaces. We prove criteria for the representability of these functors in the respective categories. As an application of adic Weil restrictions, we prove that adic N\'eron models behave well with respect to tamely ramified base change.