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

2023/12/28 by Sungyoon Cho, He Qiao, Cho, Sungyoon +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.16906

openalex publication_date 2023/12/28 · openalex created_date 2023/12/30 · openalex updated_date 2026/07/28

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.

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• Unitary Shimura varieties at ramified primes and arithmetic transfer