Endoscopic character identities for depth-zero supercuspidal L-packets

TL;DR

This paper proves the conjectural transfer of L-packets in the local Langlands correspondence for certain p-adic groups, establishing a key link between unstable and stable characters under endoscopic induction.

Contribution

It confirms the endoscopic transfer conjecture for depth-zero supercuspidal L-packets in unramified p-adic groups, extending previous theoretical frameworks.

Findings

Endoscopic induction matches unstable and stable characters.

Valid under mild residual characteristic conditions.

Supports the conjectural framework of the local Langlands correspondence.

Abstract

We prove the conjectural endoscopic transfer of L-packets for the local Langlands correspondence for pure inner forms of unramified p-adic groups and depth-zero parameters established by DeBacker and Reeder. More precisely, we show that under mild conditions on the residual characteristic, endoscopic induction identifies an unstable character of such an L-packet with the stable character of the corresponding endoscopic L-packet.