NSF PAR Search | NSF Public Access Repository

Abstract 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 algorithm to compute the $$\mathbb {F}_q$$

F_{q}

-isomorphism classes of abelian varieties over a finite field $$\mathbb {F}_q$$

F_{q}

which belong to an isogeny class determined by a characteristic polynomial hof Frobenius when his ordinary, or qis prime and hhas no real roots.

Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅

https://doi.org/10.1090/proc/16127

Marseglia, Stefano; Springer, Caleb (February 2023, Proceedings of the American Mathematical Society)

We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over

F_{2}

F_{3}

and

F_{5}

. We produce partial results for abelian varieties over a general finite field

F_{q}

. In particular, we show that certain abelian groups cannot occur as groups of rational points of abelian varieties over

F_{q}

when

q

is large. Finally, we show that every finite cyclic group arises as the group of rational points of infinitely many simple abelian varieties over

F_{2}

Full Text Available

Search for: All records