Automorphic commutator relations in relative geometric Langlands

@misc{liu2026automorphic,
  title = {{Automorphic commutator relations in relative geometric Langlands}},
  author = {Shurui Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05781},
  eprint = {2610.05781},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05781},
}

TY  - UNPB
TI  - Automorphic commutator relations in relative geometric Langlands
AU  - Shurui Liu
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05781
UR  - https://arxiv.org/abs/2610.05781
AB  - We prove the automorphic commutator relation conjectured by Liu and Wang arXiv:2504.00275, which is the geometric input for the automorphic Clifford relations in their framework relating higher period integrals to higher derivatives of L-functions over function fields. The relation was previously established only under additional cohomological vanishing assumptions and for curves of genus different from one; we remove these assumptions. The main new ingredient is a "universal-local" stage between the local and the semi-local settings: we introduce the classifying stack of formal multidisks with two ordered marked sections, and we construct universal-local analogues of the Hecke stacks, unit objects, Hecke actions and special cohomological correspondences. Fusion and purity on this stack yield a universal-local commutator identity, which is proved using only the local assumptions on the Plancherel algebra that enter the conjecture. Specialization to a curve and the six-functor formalism then give the conjecture for every smooth projective curve.
ER  -