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CATEGORIES:Number Theory Seminar
SUMMARY:The Gauss problem for central leaves - Valentijn K
aremaker (Utrecht University)
DTSTART;TZID=Europe/London:20221108T143000
DTEND;TZID=Europe/London:20221108T153000
UID:TALK180413AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/180413
DESCRIPTION:For a family of finite sets whose cardinalities ar
e naturally called class numbers\, the Gauss probl
em asks to determine the subfamily in which every
member has class number one. We study the Siegel m
oduli space of abelian varieties in characteristic
p and solve the Gauss problem for the family of c
entral leaves\, which are the loci consisting of p
oints whose associated p-divisible groups are isom
orphic. Our solution involves mass formulae\, comp
utations of automorphism groups\, and a careful an
alysis of Ekedahl-Oort strata in genus 4. This geo
metric Gauss problem is closely related to an arit
hmetic Gauss problem for genera of positive-defini
te quaternion Hermitian lattices\, which we also s
olve.
LOCATION:Centre for Mathematical Sciences\, MR13
CONTACT:Rong Zhou
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