• Corpus ID: 55590451

Torsion points on elliptic curves and tame semistable coverings

  title={Torsion points on elliptic curves and tame semistable coverings},
  author={Paul Alexander Helminck},
  journal={arXiv: Algebraic Geometry},
  • P. A. Helminck
  • Published 28 February 2018
  • Mathematics
  • arXiv: Algebraic Geometry
In this paper, we study tame Galois coverings of semistable models that arise from torsion points on elliptic curves. These coverings induce Galois morphisms of intersection graphs and we express the decomposition groups of the edges in terms of the reduction type of the elliptic curve. To that end, we first define the reduction type of an elliptic curve $E/K(C)$ on a subgraph of the intersection graph $\Sigma(\mathcal{C})$ of a strongly semistable model $\mathcal{C}$. In particular, we define… 


Tropicalizing tame degree three coverings of the projective line
In this paper, we study the problem of tropicalizing tame degree three coverings of the projective line. Given any degree three covering $C\longrightarrow{\mathbb{P}^{1}}$, we give an algorithm that
Tropicalizing abelian covers of algebraic curves
In this thesis, we study the Berkovich skeleton of an algebraic curve over a discretely valued field $K$. We do this using coverings $C\rightarrow{\mathbb{P}^{1}}$ of the projective line. To study
Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta
Let K be an algebraically closed, complete non-Archimedean field. The purpose of this paper is to carefully study the extent to which finite morphisms of algebraic K-curves are controlled by certain
On the structure of nonarchimedean analytic curves
Let K be an algebraically closed, complete nonarchimedean field and let X be a smooth K-curve. In this paper we elaborate on several aspects of the structure of the Berkovich analytic space X^an. We
Models of Curves and Finite Covers
Let K be a discrete valuation field with ring of integers O K .Letf : X ! Y be a finite morphism of curves over K. In this article, we study some possible relationships between the models over O K of
Advanced Topics in the Arithmetic of Elliptic Curves
In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational
Tropical superelliptic curves
Abstract We present an algorithm for computing the Berkovich skeleton of a superelliptic curve yn = f(x) over a valued field. After defining superelliptic weighted metric graphs, we show that each
§1.1. Motivation. The purpose of these notes is to explain the definition and basic properties of the Néron model A of an abelian variety A over a global or local field K. We also give some idea of
The arithmetic of elliptic curves
  • J. Silverman
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1986
It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Theory of Groups of Finite Order
Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation