Given a prime power $ q $ and $ n\gg 1$, we prove that every integer in a large subinterval
of the Hasse--Weil interval $[(\sqrt {q}-1)^{2n},(\sqrt {q}+ 1)^{2n}] $ is $# A (\mathbb {F} _q) …

We study the groups of rational points of abelian varieties defined over a finite field $\mathbb
{F} _q $ whose endomorphism rings are commutative, or, equivalently, whose isogeny …

Let A be an abelian variety over a finite field k with| k|= q= pm. Let π∈ End k (A) denote the
Frobenius and let v= q π− 1 denote Verschiebung. Suppose the Weil q-polynomial of A is …

Every positive integer is the order of an ordinary abelian variety over $${{\mathbb {F}}}_2$$ |
Research in Number Theory Skip to main content SpringerLink Log in Menu Find a journal …

We prove that for every positive integer m, there exist infinitely many simple abelian varieties
over F2 of order m. The method is constructive, building on the work of Madan–Pal in the …

We prove that for every positive integer $ m $, there exist infinitely many simple abelian
varieties over $\mathbb {F} _2 $ of order $ m $. The method is constructive, building on the …