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SUMMARY:The Gauss problem for central leaves - Valentijn Karemaker (Utrech
 t University)
DTSTART:20221108T143000Z
DTEND:20221108T153000Z
UID:TALK180413@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:For a family of finite sets whose cardinalities are naturally 
 called class numbers\, the Gauss problem asks to determine the subfamily i
 n which every member has class number one. We study the Siegel moduli spac
 e of abelian varieties in characteristic p and solve the Gauss problem for
  the family of central leaves\, which are the loci consisting of points wh
 ose associated p-divisible groups are isomorphic. Our solution involves ma
 ss formulae\, computations of automorphism groups\, and a careful analysis
  of Ekedahl-Oort strata in genus 4. This geometric Gauss problem is closel
 y related to an arithmetic Gauss problem for genera of positive-definite q
 uaternion Hermitian lattices\, which we also solve.
LOCATION:Centre for Mathematical Sciences\, MR13
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