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Cuspidal sheaves on the stack of L-parameters
Abstract
We introduce the notion of cuspidal coherent sheaves on the moduli stack of local L-parameters. We give a complete classification and relate them to Lusztig's cuspidal local systems (or character sheaves). Under the categorical local Langlands conjecture, these sheaves are expected to correspond to supercuspidal representations supported at basic points. We also construct semiorthogonal decompositions of the category of coherent sheaves on the moduli stack of L-parameters that conjecturally match the semiorthogonal decompositions of sheaves on BunG coming from the stratification by the Kottwitz set and Bernstein decomposition of representation categories.
Related
- Cuspidal Class Number Formulae for Intermediate Modular Curves of Prime Level
- Properness of the Cuspidal Hilbert Eigenvariety
- An analogue of Γ-function for irreducible cuspidal representations of the group GL(2) over a two-dimensional local field
- EKR Results for Cuspidal Representations of GL2(q)
- Residual finiteness and cuspidal cohomology of Picard modular surfaces
BibTeX
@misc{meli2026cuspidal,
title = {{Cuspidal sheaves on the stack of L-parameters}},
author = {Alexander Bertoloni Meli and Teruhisa Koshikawa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00220},
eprint = {2611.00220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00220},
}
RIS
TY - UNPB
TI - Cuspidal sheaves on the stack of L-parameters
AU - Alexander Bertoloni Meli
AU - Teruhisa Koshikawa
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00220
UR - https://arxiv.org/abs/2611.00220
AB - We introduce the notion of cuspidal coherent sheaves on the moduli stack of local L-parameters. We give a complete classification and relate them to Lusztig's cuspidal local systems (or character sheaves). Under the categorical local Langlands conjecture, these sheaves are expected to correspond to supercuspidal representations supported at basic points. We also construct semiorthogonal decompositions of the category of coherent sheaves on the moduli stack of L-parameters that conjecturally match the semiorthogonal decompositions of sheaves on Bun_G coming from the stratification by the Kottwitz set and Bernstein decomposition of representation categories.
ER -