On a duality theorem of Schneider-Stuhler

TL;DR

This paper generalizes a duality theorem for Ext groups in smooth representations of p-adic groups, extending its applicability from irreducible to all smooth representations using homological algebra techniques.

Contribution

It broadens the Schneider-Stuhler duality theorem to encompass all smooth representations, not just irreducible ones, via homological algebra methods.

Findings

Extended duality theorem to all smooth representations.

Reduced assumptions needed for the duality result.

Provided a homological algebra framework for the generalization.

Abstract

We extend a duality theorem of Schneider-Stuhler about $Ext^i[\pi_1,\pi_2]$ proved there for smooth representations of a $p$-adic group $G$ with central characters to all smooth representations assuming their result for only irreducible representations by generalities in homological algebra.