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

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