Kudla-Rapoport conjecture for unramified maximal parahoric level

Abstract

We prove the Kudla-Rapoport conjecture for unramified unitary groups with maximal parahoric level structure. Our approach differs from the local proof given in Li-W.Zhang. We reduce the conjecture to a global intersection problem using local-global compatibility. Then we apply an inductive procedure based on the modularity of generating series of global special divisors. This strategy follows the framework developed in the proof of the arithmetic fundamental lemma from W.Zhang and Mihatsch-W.Zhang and arithmetic transfer identities from Z.Zhang and Luo-Mihatsch-Z.Zhang.