Semistable models of elliptic curves over residue characteristic 2

Jeffrey Yelton

doi:10.4153/S0008439520000326

Semistable models of elliptic curves over residue characteristic 2

Number Theory 2021-07-01 v3

Authors: Jeffrey Yelton

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Given an elliptic curve $E$ in Legendre form $y^2 = x(x - 1)(x - \lambda)$ over the fraction field of a Henselian ring $R$ of mixed characteristic $(0, 2)$ , we present an algorithm for determining a semistable model of $E$ over $R$ which depends only on the valuation of $\lambda$ . We provide several examples along with an easy corollary concerning $2$ -torsion.

Keywords

elliptic curves semistable models legendre form henselian ring mixed characteristic valuation 2-torsion

Cite

@article{arxiv.1905.05705,
  title  = {Semistable models of elliptic curves over residue characteristic 2},
  author = {Jeffrey Yelton},
  journal= {arXiv preprint arXiv:1905.05705},
  year   = {2021}
}

Comments

7 pages, 5 citations. This paper assumes only an elementary knowledge of elliptic curves and discrete valuation rings. This is the version published Canadian Mathematical Bulletin. It differs from the previous version mainly in two additional references with a brief discussion of each

Semistable models of elliptic curves over residue characteristic 2

Abstract

Keywords

Cite

Comments

Related papers