Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 5

Special Issue in honor of Professor Benedict Gross’s 70th birthday

Guest Editors: Zhiwei Yun, Shouwu Zhang, and Wei Zhang

More Arithmetic Fundamental Lemma conjectures: the case of Bessel subgroups

Pages: 2279 – 2336

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n5.a8


Wei Zhang (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.)


We define some formal moduli spaces of quasi-isogenies of isoclinic $p$-divisible groups with a non-reductive group as the “structure group”. We then formulate new Arithmetic Fundamental Lemma conjectures for Bessel subgroups in the context of the arithmetic Gan–Gross–Prasad conjectures. Some (very limited) evidence is presented.


local Shimura variety, arithmetic Gan–Gross–Prasad conjecture, Arithmetic Fundamental Lemma, Bessel cycle, orbital integral

2010 Mathematics Subject Classification

Primary 11F67, 11G40. Secondary 14G35.

The author is supported by NSF DMS #1901642.

Received 4 August 2021

Received revised 3 January 2022

Accepted 12 January 2022

Published 12 January 2023