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UID:8175@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150205T110000
DTEND;TZID=Europe/Paris:20150205T120000
DTSTAMP:20241120T210055Z
URL:https://www.i2m.univ-amu.fr/evenements/isogeny-graphs-with-maximal-rea
 l-multiplication/
SUMMARY:Sorina Ionica (...): Isogeny graphs with maximal real multiplicatio
 n
DESCRIPTION:Sorina Ionica: An isogeny graph is a graph whose vertices are p
 rincipally polarized abelian varieties and whose edges are isogenies betwe
 en these varieties. In his thesis\, David Kohel described the structure of
  isogeny graphs for elliptic curves and showed that one may compute the en
 domorphism ring of an elliptic curve defined over a finite field by using 
 a depth first search algorithm in the graph. In dimension 2\, the structur
 e of isogeny graphs is less understood and existing algorithms for computi
 ng endomorphism rings are very expensive. We fully describe isogeny graphs
  of genus 2 Jacobians\, with maximal real multiplication. Over finite fiel
 ds\, we derive a depth first search algorithm for computing endomorphism r
 ings locally at prime numbers\, if the real multiplication is maximal. To 
 the best of our knowledge\, this is the first DFS-based algorithm in genus
  2. This is joint work with Emmanuel Thomé.\n\nSorina Ionica\, Laboratoir
 e MIS\, Universite de Picardie\, Amiens\n\n
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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