Number of rational points of a singular curve
HTML articles powered by AMS MathViewer
- by W. A. Zúñiga Galindo PDF
- Proc. Amer. Math. Soc. 126 (1998), 2549-2556 Request permission
Abstract:
In this paper, we give a bound for the number of rational points of a complete, geometrically irreducible, algebraic curve defined over a finite field. We compare it with other known bounds and discuss its sharpness. We also show that the asymptotic Drinfeld-Vladut bound can be generalized to the case of singular curves.References
- Yves Aubry and Marc Perret, A Weil theorem for singular curves, Arithmetic, geometry and coding theory (Luminy, 1993) de Gruyter, Berlin, 1996, pp. 1–7. MR 1394921
- S. G. Vlèduts and V. G. Drinfel′d, The number of points of an algebraic curve, Funktsional. Anal. i Prilozhen. 17 (1983), no. 1, 68–69 (Russian). MR 695100
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- Jean-Pierre Serre, Zeta and $L$ functions, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 82–92. MR 0194396
- Serre, J.P., Rational points on curves over finite fields, notes by Fernando Q. Gôuvea, unpublished.
- Jean-Pierre Serre, Algebraic groups and class fields, Graduate Texts in Mathematics, vol. 117, Springer-Verlag, New York, 1988. Translated from the French. MR 918564, DOI 10.1007/978-1-4612-1035-1
- Karl-Otto Stöhr, On the poles of regular differentials of singular curves, Bol. Soc. Brasil. Mat. (N.S.) 24 (1993), no. 1, 105–136. MR 1224302, DOI 10.1007/BF01231698
Additional Information
- W. A. Zúñiga Galindo
- Affiliation: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro-R.J., Brazil
- Address at time of publication: Universidad Autónoma de Bucaramanga, Laboratorio de Computo Especializado, A.A.1642, Bucaramanga, Colombia
- Email: wzuniga@bumanga.unab.edu.co
- Received by editor(s): October 17, 1995
- Received by editor(s) in revised form: January 31, 1997
- Additional Notes: The author thanks Prof. Karl-Otto Stöhr for many helpful discussions, and the referee for his or her useful comments. Supported by CNPq-Brazil and COLCIENCIAS-Colombia
- Communicated by: William W. Adams
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2549-2556
- MSC (1991): Primary 11G20; Secondary 14H25
- DOI: https://doi.org/10.1090/S0002-9939-98-04333-0
- MathSciNet review: 1451803