Non-existence of a curve over

of genus 5 with 14 rational points

Author:
Kristin Lauter

Journal:
Proc. Amer. Math. Soc. **128** (2000), 369-374

MSC (1991):
Primary 11R58, 14G10

DOI:
https://doi.org/10.1090/S0002-9939-99-05351-4

Published electronically:
July 6, 1999

MathSciNet review:
1664414

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that an absolutely irreducible, smooth, projective curve of genus over with rational points cannot exist.

**1.**N. Bourbaki,*Algèbre*, chap. IV, Hermann, Paris, 1950. MR**12:6d****2.**R. Fuhrmann, F. Torres,*The genus of curves over finite fields with many rational points*, manuscripta math.**89**(1996), p. 103-106. MR**96m:11046****3.**Y. Ihara,*Some remarks on the number of rational points of algebraic curves over finite fields*,*J. Fac. Sci. Tokyo*(1981), p. 721-724. MR**28****84c:14016****4.**J. Milne,*Etale Cohomology*. Princeton University Press: Princeton, NJ, 1980. MR**81j:14002****5.**R. Schoof,*Algebraic curves and coding theory*, UTM**336**, Univ. of Trento, 1990.**6.**J.-P. Serre,*Rational Points on curves over finite fields*. Notes by F. Gouvea of lectures at Harvard University, 1985.**7.**J.-P. Serre, Letter to K. Lauter, December 3, 1997.**8.**H.M. Stark,*On the Riemann Hypothesis in Hyperelliptic Function Fields*, Proc. AMS Symp. Pure Math.**24**(1973), p. 285-302. MR**48:11119****9.**H. Stichtenoth and C.P. Xing,*The Genus of Maximal Function Fields over Finite Fields*, manuscripta math.**86**(1995), p. 217-224. MR**95m:11131**

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Additional Information

**Kristin Lauter**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

Email:
klauter@math.lsa.umich.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05351-4

Received by editor(s):
April 6, 1998

Published electronically:
July 6, 1999

Additional Notes:
The author thanks René Schoof and Jean-Pierre Serre for their help and suggestions.

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society