7 citations · 11 across the 5 of their papers we have counts for
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Point counts of abelian varieties over finite fields determining their zeta function
Shiva Chidambaram, Timo Keller
Let be an abelian variety of dimension over a finite field . We show that if is sufficiently large relative to , the point counts $\#A(\mathbf{F}_{…
Computing quadratic points on modular curves
Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs +3
In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N…
Specialization of Mordell-Weil ranks of abelian schemes over surfaces to curves
Timo Keller
Using the Shioda-Tate theorem and an adaptation of Silverman's specialization theorem, we reduce the specialization of Mordell-Weil ranks for abelian varieties over fields finitely…
On the -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…
Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings
Nikola Adžaga, Shiva Chidambaram, Timo Keller +1
We complete the computation of all -rational points on all the maximal Atkin-Lehner quotients such that the quotient is hyperelliptic. To achieve this,…
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 of modular curves by their Fricke involutions to provably compute all the rational points of these curv…
On an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes over higher dimensional bases over finite fields
Timo Keller
We formulate an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields of chara…
On the Tate-Shafarevich group of Abelian schemes over higher dimensional bases over finite fields
Timo Keller
We study analogues for the Tate-Shafarevich group for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields.