The endoscopic character identity for even special orthogonal groups

TL;DR

This paper proves the endoscopic character identity for non-quasisplit even special orthogonal groups by reducing to known cases, advancing the understanding of local Langlands correspondence compatibility.

Contribution

It establishes the endoscopic character identity for non-quasisplit even special orthogonal groups, linking local-global principles with Arthur's multiplicity formula.

Findings

Reduces non-quasisplit case to quasisplit and real cases.

Utilizes local-global compatibility and Arthur's multiplicity formula.

Supports compatibility between Fargues--Scholze and classical local Langlands.

Abstract

We establish the endoscopic character identity for bounded $A$-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the real Adam--Johnson case by combining local-global compatibility principle with Arthur's multiplicity formula for non-quasisplit even special orthogonal groups established by Chen and Zou in arXiv:2103.07956. This result plays a key role in the author's work arXiv:2503.04623 on the compatibility between the Fargues--Scholze local Langlands correspondence and classical local Langlands correspondence for even special orthogonal groups.