Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-01T22:31:32.869Z Has data issue: false hasContentIssue false
  • English
  • Français

On Unramified Separable Abelian p-Extensions of Function Fields I

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Rights & Permissions [Opens in a new window]

Extract

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 k be an algebraically closed field of characteristic p>0. Let K/k be a function field of one variable and L/K be an unramified separable abelian extension of degree pr over K. The galois automorphisms ε1, …, εpr of L/K are naturally extended to automorphisms η(ε1), … , η(εpr) of the jacobian variety JL of L/k. If we take a svstem of p-adic coordinates on JL, we get a representation {Mp(η(εv))} of the galois group G(L/K) of L/K over p-adic integers.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 14 , February 1959 , pp. 223 - 234
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[1] Diederichsen, , Über die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Aquivalenz, Abh. Math. Hamb. Sem. Bd. 85 (1940).Google Scholar
[2] Morikawa, H., Generalized jacobian varieties and separable abelian extensions of function fields, Nagoya Math. Jour. vol. 12 (1957).Google Scholar
[3] Safarevic, , On p-extensions, Math. Sbornik N.S. 20(62), (1947).Google Scholar