Geometrization of Kottwitz-Shelstad transfer and Vogan's conjecture on local Arthur packets
Abstract
We give a geometric analogue of Kottwitz-Shelstad transfer for a general class of reductive groups over p-adic fields with cyclic component groups of trivial or prime order. We prove that this geometric transfer coincides with Kottwitz-Shelstad transfer, adapted to the language of disconnected groups, assuming the local Langlands correspondence satisfying certain desiderata, including the Kazhdan-Lusztig hypothesis for the ambient group and its endoscopic groups. As an application of this geometrization, we prove Vogan's conjecture on local Arthur packets over p-adic fields: for quasisplit classical groups and their pure inner forms, all local Arthur packets are ABV-packets, and the distributions attached to these ABV-packets of Arthur type satisfy Arthur's local conjectures on twisted endoscopic character relations. This demonstrates the following general principle: for any reductive group G over a local field, an Arthur packet should be defined as an ABV-packet of Arthur type, equipped with the endoscopic pairing calculated by traces of actions on vanishing cycles or microlocalizations.
Related
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BibTeX
@misc{cunningham2026geometrization,
title = {{Geometrization of Kottwitz-Shelstad transfer and Vogan's conjecture on local Arthur packets}},
author = {Clifton Cunningham and Alexander Hazeltine and Baiying Liu and Chi-Heng Lo and Mishty Ray and Bin Xu and Jörg Schürmann},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03342},
eprint = {2611.03342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03342},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometrization of Kottwitz-Shelstad transfer and Vogan's conjecture on local Arthur packets
AU - Clifton Cunningham
AU - Alexander Hazeltine
AU - Baiying Liu
AU - Chi-Heng Lo
AU - Mishty Ray
AU - Bin Xu
AU - Jörg Schürmann
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03342
UR - https://arxiv.org/abs/2611.03342
AB - We give a geometric analogue of Kottwitz-Shelstad transfer for a general class of reductive groups over p-adic fields with cyclic component groups of trivial or prime order. We prove that this geometric transfer coincides with Kottwitz-Shelstad transfer, adapted to the language of disconnected groups, assuming the local Langlands correspondence satisfying certain desiderata, including the Kazhdan-Lusztig hypothesis for the ambient group and its endoscopic groups. As an application of this geometrization, we prove Vogan's conjecture on local Arthur packets over p-adic fields: for quasisplit classical groups and their pure inner forms, all local Arthur packets are ABV-packets, and the distributions attached to these ABV-packets of Arthur type satisfy Arthur's local conjectures on twisted endoscopic character relations. This demonstrates the following general principle: for any reductive group G over a local field, an Arthur packet should be defined as an ABV-packet of Arthur type, equipped with the endoscopic pairing calculated by traces of actions on vanishing cycles or microlocalizations.
ER -