A proof of the Kudla-Rapoport conjecture for Krämer models

Abstract

We prove the Kudla--Rapoport conjecture for Krämer models of unitary Rapoport--Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Krämer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel--Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura vartieties associated to unimodular hermitian lattices over imaginary quadratic fields.

82pp, final version, to appear in Invent. Math