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arXiv:math/0104086 [math.AG]AbstractReferencesReviewsResources

The maximum or minimum number of rational points on curves of genus three over finite fields

Kristin Lauter, Jean-Pierre Serre

Published 2001-04-07Version 1

We show that for all finite fields F_q, there exists a curve C over F_q of genus 3 such that the number of rational points on C is within 3 of the Serre-Weil upper or lower bound. For some q, we also obtain improvements on the upper bound for the number of rational points on a genus 3 curve over F_q.

Comments: 28 pages including the appendix. Main paper by Kristin Lauter, appendix by Jean-Pierre Serre
Journal: Compositio Mathematica 134 (p. 87-111) 2002
Categories: math.AG, math.NT
Subjects: 14G45, 11G10, 14K15, 11D45
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