Ordinary abelian varieties: isogeny graphs and polarizations

Abstract: In this talk we introduce briefly Deligne's correspondence between ordinary abelian varieties defined over finite fields and a certain category of $\mathbb{Z}$-modules. Then we show how to use this correspondence to compute isogenies between such abelian varieties, including polarizations. Finally, we will discuss phenomena that arise for higher dimensional abelian varieties but not elliptic curves, and discuss features of isogeny graphs in this setting.

Mathematics

Audience: researchers in the topic

Séminaire GAATI