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

• Gerard van der Geer ^[1] ; Shushi Harashita ^[2]
  1. [1] University of Amsterdam

     University of Amsterdam

     Países Bajos

     
  2. [2] Yokohama National University

     Yokohama National University

     Naka Ku, Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01095-w
• Enlaces
  • Texto completo
• Resumen

  • 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 of dimension g 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 also determine the factor for g = 4.

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