Schwartz spaces on L-monoids: non-Archimedean

Chun-Hsien Hsu; HaoYun Yao

Schwartz spaces on L-monoids: non-Archimedean

Number Theory 2026-07-30 v1 Representation Theory

Authors: Chun-Hsien Hsu , HaoYun Yao

Abstract

We complete the Braverman-Kazhdan-Ng\^{o} program over non-Archimedean local fields assuming local Langlands conjecture for tempered representations and a natural assumption on the $\gamma$ -factors of non-supercuspidal discrete series. In particular, the program is complete unconditionally for general linear groups.

Keywords

Schwartz space L-monoid non-Archimedean local field local Langlands conjecture Braverman-Kazhdan-Ngo program

Cite

@article{arxiv.2607.28507,
  title  = {Schwartz spaces on L-monoids: non-Archimedean},
  author = {Chun-Hsien Hsu and HaoYun Yao},
  journal= {arXiv preprint arXiv:2607.28507},
  year   = {2026}
}

Comments

65 pages. Comments welcome!