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Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
Abstract
This is the first of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. In this first part, we construct (inspired by, and extending, Kaletha's explicit Local Langlands Correspondence for non-singular supercuspidal representations) semisimple inertial L-parameters for all cuspidal representations arising from Yu's constructions, with arbitrary coefficients. We then establish a characterization of this correpondence in terms of certain functoriality properties. This characterization will be used in the sequel paper in order to compute the Fargues--Scholze correspondence after restriction to inertia.
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BibTeX
@misc{cotner2026local,
title = {{Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization}},
author = {Sean Cotner and Tony Feng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16381},
eprint = {2609.16381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16381},
}
RIS
TY - UNPB
TI - Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
AU - Sean Cotner
AU - Tony Feng
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.16381
UR - https://arxiv.org/abs/2609.16381
AB - This is the first of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. In this first part, we construct (inspired by, and extending, Kaletha's explicit Local Langlands Correspondence for non-singular supercuspidal representations) semisimple inertial L-parameters for all cuspidal representations arising from Yu's constructions, with arbitrary coefficients. We then establish a characterization of this correpondence in terms of certain functoriality properties. This characterization will be used in the sequel paper in order to compute the Fargues--Scholze correspondence after restriction to inertia.
ER -