More Arithmetic Fundamental Lemma conjectures: the case of Bessel subgroups

TL;DR

This paper introduces new conjectures related to the Arithmetic Fundamental Lemma for Bessel subgroups, expanding the scope of the arithmetic Gan-Gross-Prasad program with formal moduli spaces of p-divisible groups.

Contribution

It formulates novel conjectures for Bessel subgroups within the arithmetic Fundamental Lemma framework, involving formal moduli spaces with non-reductive structure groups.

Findings

Some limited evidence supporting the conjectures

Definition of formal moduli spaces for isoclinic p-divisible groups

Extension of the AFL to Bessel subgroup context

Abstract

We define some formal moduli space 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.