number theory

Schwartz spaces on L-monoids: non-Archimedean

arXiv:2607.28507

summary

The paper completes the Braverman‑Kazhdan‑Ngô program for non‑Archimedean local fields, assuming the local Langlands conjecture for tempered representations and a condition on γ‑factors, and provides an unconditional result for general linear groups.

Abstract

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

66 pages. Fix minor typos fixed. Strengthen results in section 6

Topics & keywords

#schwartz spaces#l-monoids#non-archimedean local fields#braverman-kazhdan program#local langlands correspondence#gamma factorsSchwartz spaceL-monoidnon-Archimedeanlocal Langlands conjectureγ‑factorstempered representationsGL_n
Schwartz spaces on L-monoids: non-Archimedean · wovepaper