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SUMMARY:Bogdan Adrian Dina (Universität Ulm) and Sorina Ionica (Universit
 é de Picardie)
DTSTART:20200702T163000Z
DTEND:20200702T170000Z
DTSTAMP:20260423T200601Z
UID:ANTS14/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/16/">
 Genus 3 hyperelliptic curves with CM via Shimura reciprocity</a>\nby Bogda
 n Adrian Dina (Universität Ulm) and Sorina Ionica (Université de Picardi
 e) as part of Algorithmic Number Theory Symposium (ANTS XIV)\n\n\nAbstract
 \nUp to isomorphism over $C$\, every simple principally polarized abelian 
 variety of dimension 3 is the Jacobian of a smooth projective curve of gen
 us 3. Furthermore\, this curve is either a hyperelliptic curve or a plane 
 quartic. Given a sextic CM field $K$\, we show that if there exists a hype
 relliptic Jacobian with CM by $K$\, then all principally polarized abelian
  varieties that are Galois conjugated to it are hyperelliptic. Using Shimu
 ra's reciprocity law\, we give an algorithm for computing approximations o
 f the invariants of the initial curve\, as well as their Galois conjugates
 . This allows us ton define and compute class polynomials for genus 3 hype
 relliptic curves with CM.\n\nThe slides used in the pre-recorded session a
 re available <a href="https://math.mit.edu/~drew/ANTSXIV/Genus3Hyperellipt
 icVideoSlides.pdf">here</a>.\n\nChairs: Wouter Castryck and Chloe Martinda
 le\n
LOCATION:https://researchseminars.org/talk/ANTS14/16/
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