3 papers
math.NT2026
Reduction Types of Genus 2 Curves
Edwina Aylward, Lilybelle Cowland Kellock, Vladimir Dokchitser +1
Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tab…
math.NT2024
A note on the parity conjecture and base change
Vladimir Dokchitser
The parity conjecture predicts that the parity of the rank of an abelian variety is determined by its global root number, that is by the sign in the conjectural functional equation…
math.NT2024
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.…