Singularity and arithmetic transfers at parahoric levels

For any parahoric $\mathbb Z_{p^2}/ \mathbb Z_p$ hermitian lattice, I will formulate and prove an arithmetic transfer identity relating derived intersection numbers on relevant Rapoport--Zink spaces to derivatives of relevant orbital integrals, including the arithmetic fundamental lemma as a special case. As our moduli spaces are usually singular, we resolve the singularity (similar to the Atiyah flop) to define well-behaved intersection numbers.

I will focus on local pictures. These identities have applications towards the arithmetic GGP conjecture for unitary groups, which generalizes the Gross-Zaiger formula on Shimura curves to higher dimensions.