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math.NT2022
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…
math.NT2022
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…
math.NT2022
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…