6 papers · 1 filter
Ordinary abelian varieties: isogeny graphs and polarizations
Edgar Costa, Taylor Dupuy, Stefano Marseglia +2
Given an integer and an ordinary isogeny class of abelian varieties defined over a finite field with commutative -endomorphism algebra, we provide…
Isogeny graphs of abelian varieties and singular ideals in orders
Sarah Arpin, Stefano Marseglia, Caleb Springer
Famously, Kohel proved that isogeny graphs of ordinary elliptic curves are beautifully structured objects, now called volcanos. We prove graph structural theorems for abelian varie…
Weil polynomials of small degree
Stefano Marseglia
Honda and Tate showed that the isogeny classes of abelian varieties of dimension over a finite field are classified in terms of -Weil polynomials of degree $2…
Labeling abelian varieties over finite fields
Edgar Costa, Taylor Dupuy, Stefano Marseglia +2
We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism a…
Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms
Jonas Bergström, Valentijn Karemaker, Stefano Marseglia
We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with elements in a fixed isogeny class in terms of pairs c…
Computing the ideal class monoid of an order
Stefano Marseglia
There are well known algorithms to compute the class group of the maximal order of a number field and the group of invertible ideal classes of a non-maximal ord…