Arithmetic invariants of supersingular abelian varieties

Abstract: We will study the moduli space of abelian varieties in characteristic p and in particular its supersingular locus S_g. We will discuss when this locus is geometrically irreducible, thereby solving a “class number one problem” or “Gauss problem” for the number of irreducible components; and when a polarised abelian variety is determined by its p-divisible group, solving a Gauss problem for central leaves, which are the loci consisting of points whose associated p-divisible groups are isomorphic. Furthermore, Oort conjectured that all generic points of S_g have automorphism group {+/- 1}. We will present our results that settle Oort’s conjecture for g=2,3,4, and for all higher even dimensions when p >= 5. This is based on joint works with Ibukiyama and Yu.

number theory

Audience: researchers in the topic

London number theory seminar

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