S. Marseglia

activity

20182026

collaborators

6 papers

math.NT2026

Ordinary abelian varieties: isogeny graphs and polarizations

Edgar Costa, Taylor Dupuy, Stefano Marseglia +2

Given an integer $D$ and an ordinary isogeny class of abelian varieties defined over a finite field $F_{q}$ with commutative $F_{q}$ -endomorphism algebra, we provide…

math.NT2025

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…

math.NT2025

Weil polynomials of small degree

Stefano Marseglia

Honda and Tate showed that the isogeny classes of abelian varieties of dimension $g$ over a finite field $F_{q}$ are classified in terms of $q$ -Weil polynomials of degree $2…

math.NT2025

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…

math.AG2018

Computing abelian varieties over finite fields isogenous to a power

Stefano Marseglia

In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties $A$ isogenous to $B^{r}$ , where the characteristic polynomial $g$ of Frobenius of…

math.NT2018

Computing the ideal class monoid of an order

Stefano Marseglia

There are well known algorithms to compute the class group of the maximal order $O_{K}$ of a number field $K$ and the group of invertible ideal classes of a non-maximal ord…