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…
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…
Brauer relations, isogenies and parities of ranks
Alexandros Konstantinou
The present paper illustrates the utility of Brauer relations, Galois covers of curves and the theory of regulator constants in the context of studying isogenies between Jacobians…