A conjectural construction of Arthur packets in Fargues-Scholze's categorical local Langlands correspondence
Abstract
We present a conjectural construction of Arthur packets within Fargues-Scholze's framework for the categorical local Langlands correspondence (CLLC). This construction consists of three parts. We first provide an overview the main statement of the CLLC, the underlying moduli stacks -- ParG of parameters and BunG of G-bundles -- on the two sides of the correspondence, and its relation to representations of reductive p-adic groups. We then review the geometric Satake correspondence in order to define Hecke operators and the spectral action of sheaves on ParG on sheaves on BunG, and to construct semisimple parameters using excursion data. Finally, we generalize the geometric construction of Arthur packets from pushing-forward skyscraper sheaves on the regular conormal bundle of ParG over ℂ to a conjectural analogous operation on the stack of singularities on ParG over ℚ̅ℓ.
Related
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BibTeX
@misc{tam2026conjectural,
title = {{A conjectural construction of Arthur packets in Fargues-Scholze's categorical local Langlands correspondence}},
author = {Geo Kam-Fai Tam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24341},
eprint = {2608.24341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24341},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A conjectural construction of Arthur packets in Fargues-Scholze's categorical local Langlands correspondence
AU - Geo Kam-Fai Tam
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2608.24341
UR - https://arxiv.org/abs/2608.24341
AB - We present a conjectural construction of Arthur packets within Fargues-Scholze's framework for the categorical local Langlands correspondence (CLLC). This construction consists of three parts. We first provide an overview the main statement of the CLLC, the underlying moduli stacks -- Par_G of parameters and Bun_G of G-bundles -- on the two sides of the correspondence, and its relation to representations of reductive p-adic groups. We then review the geometric Satake correspondence in order to define Hecke operators and the spectral action of sheaves on Par_G on sheaves on Bun_G, and to construct semisimple parameters using excursion data. Finally, we generalize the geometric construction of Arthur packets from pushing-forward skyscraper sheaves on the regular conormal bundle of Par_G over ℂ to a conjectural analogous operation on the stack of singularities on Par_G over ℚ̅_ℓ.
ER -