Derived Langlands VI: Monomial resolutions and $2$-variable L-functions

TL;DR

This paper sketches a construction of the 2-variable Langlands L-function using monomial resolutions of admissible representations of reductive p-adic Lie groups, offering a new perspective on Langlands' theory.

Contribution

It introduces a novel approach to defining 2-variable L-functions via monomial resolutions, connecting representation theory with Langlands' framework.

Findings

Proposes a new construction method for 2-variable L-functions.

Links monomial resolutions to Langlands' admissible representations.

Provides insights into the structure of p-adic Lie group representations.

Abstract

In this brief essay a construction of the $2$-variable L-function of Langlands is sketched in terms of monomial resolutions of admissible representations of reductive locally $p$-adic Lie groups.