5 papers · 1 filter
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…
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…
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.…
Character formula for Weil representations in terms of Frobenius traces
Tim Dokchitser, Vladimir Dokchitser
It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all…
Reduction of Plane Quartics and Cayley Octads
Raymond van Bommel, Jordan Docking, Vladimir Dokchitser +2
We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p-adic criteria that efficiently…