4
$\begingroup$

Let $A$ be a supersingular abelian surface over a finite field $\mathbb{F}_q$. In that case the Neron-Severi group $NS(A\otimes\overline{\mathbb{F}_q})$ is the lattice of rank $6$. Are there methods to compute the induced action of Frobenius map $F_q$ on $NS(A\otimes\overline{\mathbb{F}_q})$?

In particular, I am interested in the Jacobian variety $J$, associated with the hyperelliptic curve $C\!: y^2 = x^5 - 1$ over a field $\mathbb{F}_p$, $p \equiv 2, 3$ $(mod$ $5)$. This is the supersingular abelian surface by Choie, Jeong, Lee, Supersingular hyperelliptic curve of genus 2 over finite fields, for example.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.