4 papers
Selmer ranks under quadratic twists satisfying the Heegner hypothesis
Alexandros Konstantinou
We investigate variations of Selmer ranks under quadratic twists satisfying the Heegner hypothesis. In particular, starting with an elliptic curve with partial -t…
On Galois covers of curves and arithmetic of Jacobians
Alexandros Konstantinou, Adam Morgan
We study the arithmetic of curves and Jacobians endowed with the action of a finite group . This includes a study of the basic properties, as -modules, of their -adic r…
Parity of ranks of Jacobians of curves
Vladimir Dokchitser, Holly Green, Alexandros Konstantinou +1
We investigate Selmer groups of Jacobians of curves that admit an action of a non-trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks.…
A note on the order of the Tate--Shafarevich group modulo squares
Alexandros Konstantinou
We investigate the order of the Tate--Shafarevich group of abelian varieties modulo rational squares. Our main result shows that every square-free natural number appears as the non…