On the arithmetic transfer conjecture for exotic smooth formal moduli spaces

TL;DR

This paper formulates and proves a local arithmetic transfer conjecture related to exotic smooth formal moduli spaces of p-divisible groups, advancing the understanding of the arithmetic Gan-Gross-Prasad conjecture in specific cases.

Contribution

It introduces a new local conjecture for exotic smooth formal moduli spaces and proves it for a unitary group in three variables.

Findings

Conjecture formulated for exotic smooth formal moduli spaces.

Proof established for the case of a unitary group in three variables.

Progress towards the arithmetic Gan-Gross-Prasad conjecture.

Abstract

In the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary group relative to a ramified quadratic extension of a p-adic field. We prove our conjecture in the case of a unitary group in three variables.