On the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level structure at unramified primes

Abstract

In this article, we prove that a version of Tate conjectures for certain Deligne-Lusztig varieties implies the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level at unramified primes. Furthermore, we prove that the Kudla-Rapoport conjecture holds unconditionally for several new cases in any dimension.

93 pages