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

Gerard van der Geer, Shushi Harashita

• 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.