PreprintarXiv licencearXiv
Local Constancy of the Betti Automorphic Category over the Moduli of Curves
Abstract
Nadler and Yun conjectured that the automorphic side of the Betti geometric Langlands correspondence forms a local system of categories over the moduli of curves. We prove this local constancy conjecture using purely microlocal methods, independent of the recently established Betti geometric Langlands conjecture. In particular, it follows that the Betti automorphic category depends only on the genus of the curve, verifying a conjecture of Ben-Zvi and Nadler.
Related
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BibTeX
@misc{færgeman2026local,
title = {{Local Constancy of the Betti Automorphic Category over the Moduli of Curves}},
author = {Joakim Færgeman and Marius Kjærsgaard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12384},
eprint = {2610.12384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12384},
}
RIS
TY - UNPB
TI - Local Constancy of the Betti Automorphic Category over the Moduli of Curves
AU - Joakim Færgeman
AU - Marius Kjærsgaard
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.12384
UR - https://arxiv.org/abs/2610.12384
AB - Nadler and Yun conjectured that the automorphic side of the Betti geometric Langlands correspondence forms a local system of categories over the moduli of curves. We prove this local constancy conjecture using purely microlocal methods, independent of the recently established Betti geometric Langlands conjecture. In particular, it follows that the Betti automorphic category depends only on the genus of the curve, verifying a conjecture of Ben-Zvi and Nadler.
ER -