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Séminaire de Théorie Algorithmique des Nombres

Responsable : Damien Robert

Page du séminaire

  • Le 30 mai 2017 à 10:00
  • Salle 385
    Benjamin Wesolowski (EPFL)
    Isogeny graphs of ordinary abelian varieties
    Fix a prime number $\ell$. Graphs of isogenies of degree a power of$\ell$ are well-understood for elliptic curves, but not forhigher-dimensional abelian varieties. We study the case of absolutelysimple ordinary abelian varieties over a finite field. We analysegraphs of so-called $\mathfrak l$-isogenies, resolving that, inarbitrary dimension, their structure is similar, but not identical, tothe ``volcanoes’’ occurring as graphs of isogenies of elliptic curves.Specializing to the case of principally polarizable abelian surfaces,we then exploit this structure to describe graphs of a particular classof isogenies known as $(\ell, \ell)$-isogenies. These results lead tonew, provable algorithms to navigate in isogeny graphs, withconsequences for the CM-method in genus 2, for computing explicitisogenies, and for the random self-reducibility of the discretelogarithm problem in genus 2 cryptography.
  • Le 6 juin 2017 à 10:00
  • Salle 385
    Philippe Moustrou (IMB)

  • Le 13 juin 2017 à 10:00
  • Salle 385
    Bernhard Schmidt (Singapore)

    Afficher 2016 - 2015 - antérieurs