The cycle class of the supersingular locus of principally polarized abelian varieties

2023/07/26 by Gerard van der Geer, van der Geer, Gerard, Shushi Harashita +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.14393

openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties in characteristic p. This formula determines this class as a monomial in the Chern classes of the Hodge bundle up to a factor that is a polynomial in p. This factor is known for g≤ 3. We determine the factor for g=4.

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