Seminariet i Algebraisk geometri och talteori

​​Valentijn Karemaker, Utrecht University: The Gauss problem for central leaves
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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 forms, which we also solve.
​​Organisers: Anders Södergren (andesod@chalmers.se) and Christian Johansson (chrjohv@chalmers.se). Please contact one of us if you wish to be informed of future seminars.
Kategori Seminarium
Plats: Euler, Skeppsgränd 3
Tid: 2022-10-05 15:15
Sluttid: 2022-10-05 16:15

Sidansvarig Publicerad: ti 04 okt 2022.