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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
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Abstract

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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