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arXiv · 2506.17907

The endoscopic character identity for even special orthogonal groups

Hao Peng
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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.

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Hao Peng. 2025-06-22. The endoscopic character identity for even special orthogonal groups. https://arxiv.org/abs/2506.17907

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