Add to ORKGInspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed ${g\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\to\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of $n$ into odd parts
Abstract We study the arithmetic of abelian varieties over K = k(t) where k is an arbitrary field. T...
Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computin...
Let p be an odd prime number and g ≥ 2 be an integer. We present an algorithm for computing explicit...
Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties de...
Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its algebraic closure. Let $n \ge...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
10 pages, comments are welcomeInternational audienceWe consider the finite set of isogeny classes of...
We discuss methods for using the Weil polynomial of an isogeny class of abelian varieties over a fin...
In this paper, we compute l-isogenies between abelian varieties over a field of characteristic diffe...
(0.1) Question Given an abelian variety A; does there exist an algebraic curve C such that there is...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
AbstractA pairing-friendly curve is a curve over a finite field whose Jacobian has small embedding d...
Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its algebraic closure. Let $n \ge...
AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the ...
Abstract We study the arithmetic of abelian varieties over K = k(t) where k is an arbitrary field. T...
Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computin...
Let p be an odd prime number and g ≥ 2 be an integer. We present an algorithm for computing explicit...
Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties de...
Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its algebraic closure. Let $n \ge...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
10 pages, comments are welcomeInternational audienceWe consider the finite set of isogeny classes of...
We discuss methods for using the Weil polynomial of an isogeny class of abelian varieties over a fin...
In this paper, we compute l-isogenies between abelian varieties over a field of characteristic diffe...
(0.1) Question Given an abelian variety A; does there exist an algebraic curve C such that there is...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first...
AbstractA pairing-friendly curve is a curve over a finite field whose Jacobian has small embedding d...
Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its algebraic closure. Let $n \ge...
AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the ...
Abstract We study the arithmetic of abelian varieties over K = k(t) where k is an arbitrary field. T...
Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computin...
Let p be an odd prime number and g ≥ 2 be an integer. We present an algorithm for computing explicit...