# Groupes analytiques rigides p-divisibles II

## TL;DR

This paper advances the theory of rigid analytic p-divisible groups over p-adic fields, connecting them to Banach-Colmez spaces and applying results to integral models of Rapoport-Zink spaces.

## Contribution

It develops methods to recover Banach-Colmez spaces from rigid analytic p-divisible groups without perfectoid spaces and proves a minimality result for integral models of unramified Rapoport-Zink spaces.

## Key findings

- Established a link between rigid analytic p-divisible groups and Banach-Colmez spaces.
- Proved a minimality result for integral models of unramified Rapoport-Zink spaces.
- Extended the theory of p-divisible groups over p-adic fields.

## Abstract

Let $K$ be a $p$-adic field. We continue to develop the theory of rigid analytic $p$-divisible groups over $K$. For example, we explain how to find back the category of Banach-Colmez spaces from rigid analytic $p$-divisible groups "in finite level" without perfectoid spaces. We then establish some results about families of rigid analytic $p$-divisible groups. This allows us to prove a "minimality" result in the sense of birationnal geometry for integral models of unramified Rapoport-Zink spaces.