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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