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Semistable models of elliptic curves over residue characteristic 2

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  29 April 2020

Jeffrey Yelton
Jeffrey Yelton*
Affiliation:
Emory University, Mathematics & Science Center, Suite E431, Atlanta, Georgia30322, USA
*
e-mail: jeffrey.yelton@emory.edu
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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 that depends only on the valuation of $\lambda $. We provide several examples along with an easy corollary concerning $2$-torsion.

MSC classification

Primary: 11G07: Elliptic curves over local fields
Secondary: 11G20: Curves over finite and local fields
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 154 - 162
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Copyright
© Canadian Mathematical Society 2020

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References

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