L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld : Decomposition cellulaire de la tour de Lubin-Tate

TL;DR

This paper constructs a p-adic integral model of the Lubin-Tate tower with infinite level, laying the groundwork for establishing an isomorphism with the Drinfeld tower and exploring its applications.

Contribution

It introduces a new p-adic equivariant integral model of the Lubin-Tate tower with infinite level, facilitating comparison with the Drinfeld tower.

Findings

Construction of a p-adic equivariant integral model of the Lubin-Tate tower.

Foundation for comparing Lubin-Tate and Drinfeld towers.

Preliminary step towards establishing their isomorphism.

Abstract

This article is the first one of a series aiming to construct an isomorphism between the p-adic Lubin-Tate and Drinfeld towers, describe this isomorphism and give applications. We construct a p-adic equivariant integral model of the Lubin-Tate tower with infinite level. This formal scheme will be later compared to another one associated to the Drinfeld tower.