For any sufficiently general family of curves over a finite field Fq and any elementary abelian
ℓ-group H with ℓ relatively prime to q, we give an explicit formula for the proportion of curves …

In this expository article we explore the relationship between Galois representations, motivic
L-functions, Mumford-Tate groups, and Sato-Tate groups, and we give an explicit …

Let be an abelian variety over of dimension such that the image of its associated absolute
Galois representation is open in. We investigate the arithmetic of the traces of the Frobenius …

Abstract In 2000, Galbraith and McKee heuristically derived a formula that estimates the
probability that a randomly chosen elliptic curve over a fixed finite prime field has a prime …

In discrete logarithm based cryptography, a method by Pohlig and Hellman allows solving
the discrete logarithm problem efficiently if the group order is known and has no large prime …

We give an efficient explicit algorithm to find the structure and generators of the maximal 2-
subgroup of the Jacobian of a genus 2 curve over a finite field of odd characteristic. We use …

Let A be a principally polarized abelian variety defined over Q with endomorphism ring
equal to Z and A [ℓ] be the group of ℓ-torsion points of A over the algebraic closure Q a. For …

Let A be a principally polarized CM abelian variety of dimension d defined over a number
field F containing the CM-field K. Let ℓ be a prime number unramified in K/Q. The Galois …

Let A be a g-dimensional abelian variety over Q whose adelic Galois representation has
open image in GSp 2 g Z ˆ. We investigate the Frobenius fields Q (π p)= End (A p)⊗ Q of the …

characteristic polynomial Page 1 173 Abelian varieties over finite fields with a specified
characteristic polynomial par JOSHUA HOLDEN RÉSUMÉ. Nous estimons la fraction des …