Timo Keller

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20212026

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math.NT2026

Point counts of abelian varieties over finite fields determining their zeta function

Shiva Chidambaram, Timo Keller

Let $A$ be an abelian variety of dimension $g$ over a finite field $F_{q}$ . We show that if $q$ is sufficiently large relative to $g$ , the $g$ point counts $\#A(\mathbf{F}_{…

math.NT2022

On the $p$ -torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields

Timo Keller

We prove a finiteness theorem for the first flat cohomology group of finite flat group schemes over integral normal proper varieties over finite fields. As a consequence, we can pr…

math.NT2021

Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6

Nikola Adžaga, Vishal Arul, Lea Beneish +4

We use the method of quadratic Chabauty on the quotients $X_{0}^{+} (N)$ of modular curves $X_{0} (N)$ by their Fricke involutions to provably compute all the rational points of these curv…

Point counts of abelian varieties over finite fields determining their zeta function

On the p-torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields

Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6

On the $p$ -torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields