24 citations · 70 across the 18 of their papers we have counts for
19 papers
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…
Abelian surfaces over finite fields containing no curves of genus or less
Elena Berardini, Alejandro Giangreco Maidana, Stefano Marseglia
We study abelian surfaces defined over finite fields which do not contain any possibly singular curve of genus less than or equal to . Firstly, we complete and expand the charac…
Local isomorphism classes of fractional ideals of orders in étale algebras
Stefano Marseglia
We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of…
Abelian varieties over finite fields and their groups of rational points
Stefano Marseglia, Caleb Springer
We study the groups of rational points of abelian varieties defined over a finite field whose endomorphism rings are commutative, or, equivalently, whose isogeny cl…
Ideal classes of orders in quaternion algebras
Stefano Marseglia, Harry Smit
We provide an algorithm that, given any order in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right -ideals, includ…
Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields
Stefano Marseglia
We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an a…
Cohen-Macaulay type of orders, generators and ideal classes
Stefano Marseglia
In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in étale algebras. We provide a bound for the type, and give formulas to compute it. We relate the…
Every finite abelian group is the group of rational points of an ordinary abelian variety over , and
Stefano Marseglia, Caleb Springer
We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over , and . We produce…
Polarizations of abelian varieties over finite fields via canonical liftings
Jonas Bergström, Valentijn Karemaker, Stefano Marseglia
We describe all polarizations for all abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the isogeny…
Products and Polarizations of Super-Isolated Abelian Varieties
Stefano Marseglia, Travis Scholl
In this paper we study super-isolated abelian varieties, that is, abelian varieties over finite fields whose isogeny class contains a single isomorphism class. The goal of this pap…
Computing base extensions of ordinary abelian varieties over finite fields
Stefano Marseglia
We study base field extensions of ordinary abelian varieties defined over finite fields using the module theoretic description introduced by Deligne. As applications we give algori…
Super-multiplicativity of ideal norms in number fields
Stefano Marseglia
In this article we study inequalities of ideal norms. We prove that in a subring of a number field every ideal can be generated by at most elements if and only if the ideal…
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 isogenous to , where the characteristic polynomial of Frobenius of…
Computing square-free polarized abelian varieties over finite fields
Stefano Marseglia
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field whose characteristic polynomial (of Frobenius) is square-…
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…