Inductive construction of supercuspidal $L$-packets

TL;DR

This paper proves the surjectivity of a recently constructed local Langlands parameterization for split reductive groups over function fields, assuming a stable twisted trace formula, advancing understanding of local Langlands correspondence.

Contribution

It establishes the surjectivity of the semisimple local Langlands parameterization for split groups in large characteristic, building on recent constructions by Genestier--Lafforgue and Fargues--Scholze.

Findings

Proves surjectivity of the local Langlands parameterization.

Assumes a stable twisted trace formula for function fields.

Advances the understanding of local Langlands correspondence in positive characteristic.

Abstract

Genestier--Lafforgue and Fargues--Scholze have constructed a semisimple local Langlands paramterization for reductive groups over equicharacteristic local fields. Assuming a version of the stable twisted trace formula for function fields, we prove the surjectivity of this parameterization for split groups in sufficiently large characteristic.