A comparison between pro-$p$ Iwahori-Hecke modules and mod $p$ representations

TL;DR

This paper establishes an equivalence of categories linking specific modules over pro-$p$ Iwahori-Hecke algebras with mod $p$ representations, advancing understanding of their structural relationship.

Contribution

It introduces a new categorical equivalence between modules of pro-$p$ Iwahori-Hecke algebras and mod $p$ representations, clarifying their connection.

Findings

Categorical equivalence between modules and representations

Enhanced understanding of pro-$p$ Iwahori-Hecke algebra structures

Framework for future research in mod $p$ representation theory

Abstract

We give an equivalence of categories between certain subcategories of modules of pro-$p$-Iwahori Hecke algebras and modulo $p$ representations.