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Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization
Abstract
This is the second of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. We compute the Tate cohomology of cuspidal representations arising from Yu's construction. Combining this with modular functoriality in the Local Langlands Correspondence, independence of ℓ, and the partial characterization of the Local Langlands Correspondence established in the first paper, we compare the Fargues--Scholze and Kaletha parametrizations. Among the consequences, we deduce that the Fargues--Scholze correspondence has finite fibers and is surjective onto inertial L-parameters.
Related
- Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
- A conjectural construction of Arthur packets in Fargues-Scholze's categorical local Langlands correspondence
- The Categorical Fargues-Scholze Correspondence at Generic Parameters
- On the Langlands--Kottwitz--Scholze method
- Meromorphic vector bundles on the Fargues–Fontaine curve
BibTeX
@misc{cotner2026local,
title = {{Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization}},
author = {Sean Cotner and Tony Feng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16387},
eprint = {2609.16387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16387},
}
RIS
TY - UNPB
TI - Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization
AU - Sean Cotner
AU - Tony Feng
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.16387
UR - https://arxiv.org/abs/2609.16387
AB - This is the second of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. We compute the Tate cohomology of cuspidal representations arising from Yu's construction. Combining this with modular functoriality in the Local Langlands Correspondence, independence of ℓ, and the partial characterization of the Local Langlands Correspondence established in the first paper, we compare the Fargues--Scholze and Kaletha parametrizations. Among the consequences, we deduce that the Fargues--Scholze correspondence has finite fibers and is surjective onto inertial L-parameters.
ER -