Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T10:54:51.411Z Has data issue: false hasContentIssue false
  • English
  • Français

On normal closures related to elliptic curves

Published online by Cambridge University Press:  09 April 2009

D. J. Lewis  and
Patrick Morton
Patrick Morton
Affiliation:
University of Michigan Ann Arbor, Michigan 48109
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.

Let F(z) be a polynomial with coefficients in a perfect field k and let K be the normal closure of k(z) over k(F). All polynomials for which the genus of K over k is one are determined; they depend in part on the characteristic of k. Some results for higher genus are given.

Subject classification (Amer. Math. Soc. (MOS) 1970): 12 F 10.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 4 , December 1978 , pp. 385 - 409
Copyright
Copyright © Australian Mathematical Society 1978

References

Bremner, A. and Morton, P. (1978), ‘Polynomial relations in characteristic p’, Quart. J. Math. Oxford (2), 29, 335–347.CrossRefGoogle Scholar
Cassels, J. W. S. (1966), ‘Diophantine equations with special reference to elliptic curves’, J. London Math. Soc. 41, 193–291.Google Scholar
Deuring, M. (1941a), ‘Die Typen der Multiplikatorenringe elliptischer Funktionenkörper’, Abh. Math. Sem. hans. Univ. 14, 197–272.CrossRefGoogle Scholar
Deuring, M. (1941b), ‘Invarianten und Normalform elliptischer Funktionenkörper’, math. Z. 47 47–56.CrossRefGoogle Scholar
Deuring, M. (1947), ‘Zur Theorie der elloptischen Funktionenkörper’, Abh. Math. Sem. Univ. Hamburg 15 211–261.Google Scholar
Hasse, H. (1934), ‘Existenz separabler zyklischer unverweigter Erweiterungskörper vom Primzahlgrad P üner elliptischen Funktionenköpern der Charakterstik p’, J. Reine angew math. 172, 77–85.Google Scholar
Hasse, H. (1936), ‘Zur Theorie der abstrakten elliptischen Funktionenkörper I, II, III’, J. Reine angew. Math. 175 55–62, 69–88, 193–208.CrossRefGoogle Scholar
Hasse, H. (1963), Zahlentheorie (Akademic Verlag, Berlin).Google Scholar
Roquette, P. (1970a), Analytic theory of elliptic functions over local fields (Hamburger Math. Einzelschriften, New Folge, Helf 1).Google Scholar
Roquette, P. (1970b), ‘Abschätzung der Automorphismenanzahl von Funktionenkörpern bei Primzahlcharakteristik’, Math. Z. 117, 157–163.Google Scholar
Stichtenoth, H. (1973), ‘Über die Automorphismengruppe eines algebraischen Funcktionenkorpers von primzahlcharakteristik I’, Arch. Math. Oberwohlfach, 24, 527–544.Google Scholar