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.
Abstract We present a relative trace formula approach to the Gross–Zagier formula and its generalization to higher-dimensional unitary Shimura vari- eties. As a crucial ingredient, we formulate a conjectural arithmetic funda- mental lemma for unitary Rapoport–Zink spaces. We prove the conjecture when the Rapoport–Zink space is associated to a unitary group in two or three variables.
Yu ZhaoJohn Abbbott CollegeVictor Rotger Universitat Polit ` ecnica de CatalunyaHenri DarmonMcGill University
Geometry and Analysis of Automorphic forms of several variables, Proceedings of the International Symposium in Honor of Takayuki Oda on the Occasion of his 60th birthday, Series on Number Theory and its applications, 7, 1-40, 2012