On the arithmetic transfer conjecture for exotic smooth formal moduli spaces

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.