27 citations · 49 across the 13 of their papers we have counts for
11 papers · 1 filter
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.…
Field change for the Cassels-Tate pairing and applications to class groups
Adam Morgan, Alexander Smith
In previous work, the authors defined a category of finite Galois modules decorated with local conditions for each global field . In this paper, given an extension $K/F…
A note on hyperelliptic curves with ordinary reduction over 2-adic fields
Vladimir Dokchitser, Adam Morgan
We study a class of semistable ordinary hyperelliptic curves over 2-adic fields and the special fibre of their minimal regular model. We show that these curves can be controlled us…
The Cassels-Tate pairing for finite Galois modules
Adam Morgan, Alexander Smith
Given a global field with absolute Galois group , we define a category whose objects are finite -modules decorated with local conditions. We define this cate…
The -rank of class groups of
Peter Koymans, Adam Morgan, Harry Smit
Let be a quadratic extension. In this paper we study the -rank of the class group , where varies over squarefree rational integers. We…
On 2-Selmer groups of twists after quadratic extension
Adam Morgan, Ross Paterson
Let be an elliptic curve with full rational 2-torsion. As d varies over squarefree integers, we study the behaviour of the quadratic twists over a fixed quadra…
A user's guide to the local arithmetic of hyperelliptic curves
Alex J. Best, L. Alexander Betts, Matthew Bisatt +8
A new approach has been recently developed to study the arithmetic of hyperelliptic curves over local fields of odd residue characteristic via combinatorial data associa…
Tate module and bad reduction
Tim Dokchitser, Vladimir Dokchitser, Adam Morgan
Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us…
Arithmetic of hyperelliptic curves over local fields
Tim Dokchitser, Vladimir Dokchitser, Céline Maistret +1
We study hyperelliptic curves y^2=f(x) over local fields of odd residue characteristic. We introduce the notion of a "cluster picture" associated to the curve, that describes the p…
Quadratic twists of abelian varieties and disparity in Selmer ranks
Adam Morgan
We study the parity of 2-Selmer ranks in the family of quadratic twists of a fixed principally polarised abelian variety over a number field. Specifically, we determine the proport…
2-Selmer Parity for Hyperelliptic Curves in Quadratic Extensions
Adam Morgan
We study the 2-parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic ex…