Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T18:55:08.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)

Published online by Cambridge University Press:  20 November 2018

Roland Miyamoto  and
Jaap Top
Roland Miyamoto
Affiliation:
Sternstr. 20, 37083 Göttingen, Germany e-mail: auer@math.usask.ca
Jaap Top
Affiliation:
IWI-RuG, P.O.Box 800, 9700AV Groningen, The Netherlands e-mail: top@math.rug.nl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.

Keywords

14H5214K1511G0711G0512J10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 428 - 444
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Auer, Roland. Ray Class Fields of Global Function Fields with Many Rational Places. Thesis at the University of Oldenburg, Germany, 1999.Google Scholar
[2] Gekeler, E.-U., Highly ramified pencils of elliptic curves in characteristic 2. Duke Math. J. 89(1997), 95–107.Google Scholar
[3] Gekeler, E.-U., Local and global ramification properties of elliptic curves in characteristics two and three. In: Algorithmic Algebra and Number Theory (Heidelberg, 1997), Springer, Berlin, 1999, pp. 49–64.Google Scholar
[4] Néron, A.,Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Inst. Hautes é tudes Sci. Publ. Math. 21(1964), 359–484.Google Scholar
[5] Ogg, A. P., Elliptic curves and wild ramification. Amer. J. Math. 89(1967), 1–21.Google Scholar
[6] Papadopoulos, I., Sur la classification de Néron des courbes elliptiques en caractéristique résiduelle 2 et 3. J. Number Theory 44(1993), 119–152.Google Scholar
[7] Saito, T., Conductor, discriminant, and the Noether formula of arithmetic surfaces. Duke Math. J. 57(1988), 151–173.Google Scholar
[8] Silverman, J. H., The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics 106, Springer-Verlag, New York, 1986.Google Scholar
[9] Silverman, J. H., Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts in Mathematics 151, Springer-Verlag, 1994.Google Scholar
[10] Stichtenoth, H., Algebraic Function Fields and Codes. Springer-Verlag, Berlin, 1993.Google Scholar
[11] Tate, J., Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular Functions of One Variable, IV, (Proc. Internat. Summer School Antwerp 1972, Birch, B. J., Kuyck, W., eds.). Lecture Notes in Math. 476, Springer, Berlin, 1975, pp. 33–52.Google Scholar