Valentijn Karemaker (Universiteit Utrecht)

Abstract:

For a family of finite sets whose cardinalities are naturally called class numbers, 
the Gauss problem asks to determine the subfamily in which every member has class number one. 
We study the Siegel moduli space of abelian varieties in characteristic p and solve the Gauss problem 
for the family of central leaves, which are the loci consisting of points whose associated p-divisible groups 
are isomorphic. Our solution involves mass formulae, computations of automorphism groups, 
and a careful analysis of Ekedahl-Oort strata in genus 4. This geometric Gauss problem is 
closely related to an arithmetic Gauss problem for genera of positive-definite quaternion Hermitian lattices, 
which we also solve.

Oberseminar Algebra und Geometrie (Frankfurt)