Endoscopic decomposition of elliptic Fargues-Scholze L-packets
Abstract
The main goal of this note is to show that the local L-packet of Fargues-Scholze [FS], corresponding to an elliptic L-parameter, has an endoscopic decomposition. Our argument is strongly motivated by a beautiful paper of Chenji Fu [Fu], where the stable case is proven. To put our results in a more general context, we also construct a general endoscopic decomposition over complex numbers based on results of Arthur, and a generalization of this decomposition over an arbitrary algebraically closed field of characteristic zero based on a recent work [KSV].
Keywords
Cite
@article{arxiv.2503.00621,
title = {Endoscopic decomposition of elliptic Fargues-Scholze L-packets},
author = {David Kazhdan and Yakov Varshavsky},
journal= {arXiv preprint arXiv:2503.00621},
year = {2025}
}
Comments
v.3, 23 pages. Revised version. Section 3 have been almost completely rewritten and became more natural, main result has been slightly strengthened, an endoscopic decomposition over an arbitrary algebraically closed field of characteristic zero is now unconditional due to a recent work [KSV]