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A Note on Relations Between the Zeta-Functions of Galois Coverings of Curves Over Finite Fields

Published online by Cambridge University Press:  20 November 2018

Amilcar Pacheco
Amilcar Pacheco*
Affiliation:
Instituto de Matemâtica Pura e Aplicada Estrada Dona Castorina 110 22460 Rio de Janeiro, RJ Brasil.
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Abstract

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Let C be a complete irreducible nonsingular algebraic curve defined over a finite field k. Let G be a finite subgroup of the group of automorphisms Aut(C) of C. We prove that certain idempotent relations in the rational group ring Q[G] imply other relations between the zeta-functions of the quotient curves C/H, where H is a subgroup of G. In particular we generalize some results of Kani in the special case of curves over finite fields.

Keywords

14G10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 282 - 285
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Accola, R. D., Two theorems on Riemann surfaces with noncyclic automorphisms groups, Proc. AMS 25 (1970), 598–602.Google Scholar
2. Bombieri, E., Hilbert's 8th problem: an analogue, in Mathematical Developments arising from Hilbert's problems, Proc. Symp. Pure Math. American Mathematical Society, 28, 269–274.Google Scholar
3. Fried, M. D., Jarden, M., Field Arithmetic, Berlin, Heidelberg, Springer-Verlag, 1986.Google Scholar
4. Kani, E., Relations between the genera and the Hasse-Witt invariants of Galois coverings of curves, Can. Math. Bull. 28 (3), 321–327 (1985).Google Scholar
5. Lang, S., Abelian Varieties, New York, Springer-Verlag, 1983.Google Scholar
6. Manin, J. I., The Hasse-Witt matrix of an algebraic curve, Trans. Amer. Math. Soc. 45, 245–264 (1965).Google Scholar
7. Silverman, J., The Arithmetic of Elliptic Curves, New York, Springer-Verlag, 1986.Google Scholar
8. Weil, A., Courbes Algébriques et Variétés Abélienes, Hermann, Paris, 1971.Google Scholar