Pure and Applied Mathematics Quarterly
Volume 18 (2022)
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
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