R\'eseaux d'induction des repr\'esentations elliptiques de Lubin-Tate

TL;DR

This paper investigates the reduction modulo l of elliptic representations related to Lubin-Tate towers, providing explicit lattices and extension graphs crucial for understanding their cohomology.

Contribution

It introduces a natural lattice obtained via parabolic induction for elliptic representations and describes the extension structure in their mod l reductions.

Findings

Explicit lattices for elliptic representations are constructed.

Graphs of extensions between irreducible sub-quotients are determined.

Connections to cohomology of Lubin-Tate towers are established.

Abstract

We study the reduction modulo $l$ of some elliptic representations; for each of these representations, we give a particular lattice naturally obtained by parabolic induction in giving the graph of extensions between its irreducible sub-quotient of its reduction modulo $l$. The principal motivation for this work, is that these lattices appear in the cohomology of Lubin-Tate towers.