N\'eron models of formally finite type

TL;DR

This paper introduces Néron models of formally finite type for uniformly rigid spaces, generalizing formal Néron models for rigid-analytic groups, and provides examples illustrating their properties.

Contribution

It defines Néron models of formally finite type for uniformly rigid spaces and demonstrates their relation to existing formal Néron models, expanding the theoretical framework.

Findings

Néron models of formally finite type generalize formal Néron models.

Examples show Néron models can lack topological finite type.

Compatibility with existing models is established.

Abstract

We introduce N\'eron models of formally finite type for uniformly rigid spaces, and we prove that they generalize the notion of formal N\'eron models for rigid-analytic groups as it was defined by Bosch and Schl\"oter. Using this compatibility result, we give examples of uniformly rigid groups whose N\'eron models are not of topologically finite type.