Mod $p$ Bernstein centres of $p$-adic groups

TL;DR

This paper proves that the center of the category of smooth mod p representations with a fixed central character of a split semisimple p-adic group is a local ring, advancing understanding of representation theory in characteristic p.

Contribution

It establishes that the center of this category is a local ring, providing new structural insights into mod p representation theory of p-adic groups.

Findings

The center of the category is a local ring.

Provides structural understanding of mod p representations.

Advances the theory of p-adic group representations.

Abstract

We prove that the centre of the category of smooth mod $p$ representations with fixed central character of a split semisimple $p$-adic group is a local ring.