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Supercuspidal blocks and the local Langlands correspondence
Abstract
Let G be a connected reductive group defined over a non-archimedean local field F, and let Reps(G(F)) be a supercuspidal Bernstein block. In this paper, we define a cohomology class [μs] represented by a 2-cocycle that encodes the equivalence class of Reps(G(F)). We then formulate a conjecture describing [μs] in terms of the enhanced L-parameter $(φ, ρ)$ attached to an irreducible representation in Reps(G(F)) via the conjectural local Langlands correspondence. Finally, we verify this conjecture for the local Langlands correspondence for non-singular supercuspidal representations constructed by Kaletha.
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BibTeX
@misc{abe2026supercuspidal,
title = {{Supercuspidal blocks and the local Langlands correspondence}},
author = {Noriyuki Abe and Kazuma Ohara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27924},
eprint = {2610.27924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27924},
}
RIS
TY - UNPB
TI - Supercuspidal blocks and the local Langlands correspondence
AU - Noriyuki Abe
AU - Kazuma Ohara
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27924
UR - https://arxiv.org/abs/2610.27924
AB - Let G be a connected reductive group defined over a non-archimedean local field F, and let Rep^s(G(F)) be a supercuspidal Bernstein block. In this paper, we define a cohomology class [μ_s] represented by a 2-cocycle that encodes the equivalence class of Rep^s(G(F)). We then formulate a conjecture describing [μ_s] in terms of the enhanced L-parameter $(φ, ρ)$ attached to an irreducible representation in Rep^s(G(F)) via the conjectural local Langlands correspondence. Finally, we verify this conjecture for the local Langlands correspondence for non-singular supercuspidal representations constructed by Kaletha.
ER -