Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T05:05:40.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Relations Between the Genera and Between the Hasse-Witt Invariants of Galois Coverings of Curves

Published online by Cambridge University Press:  20 November 2018

Ernst Kani
Ernst Kani*
Affiliation:
Mathematisches Institut, Universität HeidelbergIm Neuenheimer Feld 288 6900 Heidelberg Federal Republic Germany
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 G ⊂ Aut (C) be a (finite) group of automorphisms of a curve C defined over a field K and, for each subgroup H ≤ G, let gH denote the genus of the quotient curve CH = C/H (briefly: quotient genus of H).

In this paper we show that certain idempotent relations in the rational group ring [G] imply relations between the quotient genera {gH}H=G this generalizes two theorems of Accola. Moreover, we show that in the case of char (K) = p ≠ 0, a similar statement holds for the Hasse-Witt invariants σH of the curves CH

Keywords

14H30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 321 - 327
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Accola, R.D., Two theorems on Riemann surfaces with noncyclic automorphism groups, Proc. AMS. 25 (1970), pp. 598–602.Google Scholar
2. Mumford, D., Abelian Varieties, Oxford U Press, London, 1970.Google Scholar
3. Serre, J.-P., Local Fields, Springer Verlag, New York, 1979.Google Scholar