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Relative Hitchin fibrations and endoscopy for Unitary Friedberg--Jacquet varieties

  • Thomas Hameister
  • Spencer Leslie
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Abstract

We prove a relative fundamental lemma for the unitary symmetric variety GLn(k')backslash U2n, proving a conjecture of Leslie, Xiao, and Zhang. Our proof reduces to the Lie algebra and argues over function fields in positive characteristic, using methods from Ngo-Laumon and Ngo. In particular, we reinterpret orbital integrals in terms of the cohomology of relative affine Springer fibers and globalize this using unitary versions of Hitchin moduli spaces for symmetric pairs via a product formula. As the main global input, we prove a matching of perverse sheaves between relative Hitchin moduli spaces and their corresponding endoscopic variants.

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Cite

BibTeXRIS
BibTeX
@misc{hameister2026relative,
  title = {{Relative Hitchin fibrations and endoscopy for Unitary Friedberg--Jacquet varieties}},
  author = {Thomas Hameister and Spencer Leslie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30366},
  eprint = {2610.30366},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30366},
}
RIS
TY  - UNPB
TI  - Relative Hitchin fibrations and endoscopy for Unitary Friedberg--Jacquet varieties
AU  - Thomas Hameister
AU  - Spencer Leslie
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30366
UR  - https://arxiv.org/abs/2610.30366
AB  - We prove a relative fundamental lemma for the unitary symmetric variety GL_n(k')backslash U_2n, proving a conjecture of Leslie, Xiao, and Zhang. Our proof reduces to the Lie algebra and argues over function fields in positive characteristic, using methods from Ngo-Laumon and Ngo. In particular, we reinterpret orbital integrals in terms of the cohomology of relative affine Springer fibers and globalize this using unitary versions of Hitchin moduli spaces for symmetric pairs via a product formula. As the main global input, we prove a matching of perverse sheaves between relative Hitchin moduli spaces and their corresponding endoscopic variants.
ER  -