Regular formal moduli spaces and arithmetic transfer conjectures

TL;DR

This paper introduces new regular formal moduli spaces of p-divisible groups, formulates related arithmetic transfer conjectures including ramified cases, and proves these conjectures in low-dimensional scenarios.

Contribution

It defines regular formal moduli spaces and formulates arithmetic transfer conjectures with ramification, extending previous work and providing proofs in specific cases.

Findings

Conjectures are verified in low-dimensional cases.

New formal moduli spaces of p-divisible groups are constructed.

Extensions of the arithmetic fundamental lemma conjecture are proposed.

Abstract

We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture of the third author in the presence of ramification. These conjectures include the AT conjecture of our previous joint paper. We prove these conjectures in low-dimensional cases.