Publications (22)
Hasse principle for intersections of two quadrics via Kummer surfaces
Adam Morgan, Alexei N. Skorobogatov
We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate-Shafarevich groups.…
Semistable types of hyperelliptic curves
Tim Dokchitser, Vladimir Dokchitser, Celine Maistret +1
In this paper, we explore three combinatorial descriptions of semistable types of hyperelliptic curves over local fields: dual graphs, their quotient trees by the hyperelliptic inv…
Constructing Jacobians of rank 1
Peter Koymans, Adam Morgan
Let be a number field, let be an integer and let be a polynomial that splits into distinct linear fact…
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 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…
Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
Alex Bartel, Adam Morgan
We address several seemingly disparate problems in arithmetic geometry: the statistical behaviour of the Galois module structure of Mordell--Weil groups of a fixed elliptic curve o…
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…
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.…
Ionescu's theorem for higher rank graphs
S. Kaliszewski, Adam Morgan, John Quigg
We will define new constructions similar to the graph systems of correspondences described by Deaconu et al. We will use these to prove a version of Ionescu's theorem for higher ra…
CfAIR2: Near Infrared Light Curves of 94 Type Ia Supernovae
Andrew S. Friedman, W. M. Wood-Vasey, G. H. Marion +18
CfAIR2 is a large homogeneously reduced set of near-infrared (NIR) light curves for Type Ia supernovae (SN Ia) obtained with the 1.3m Peters Automated InfraRed Imaging TELescope (P…
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…
Cuntz-Pimsner Algebras and Twisted Tensor Products
Adam Morgan
Given two correspondences and and a discrete group which acts on and coacts on , one can define a twisted tensor product which simultaneously gene…
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…
Cuntz-Pimsner Algebras Associated to Tensor Products of Correspondences
Adam Morgan
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor prod…
A note on local formulae for the parity of Selmer ranks
Adam Morgan
In this note, we provide evidence for a certain twisted version of the parity conjecture for Jacobians, introduced in prior work of V. Dokchitser, Green, Konstantinou and the autho…
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…
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…
Hasse principle for Kummer varieties in the case of generic 2-torsion
Adam Morgan
Conditional on finiteness of relevant Shafarevich--Tate groups, Harpaz and Skorobogatov used Swinnerton-Dyer's descent-fibration method to establish the Hasse principle for Kummer…
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…
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 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…