Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21959
Kresch, A; Wetherell, J; Zieve, M E (2002). Curves of every genus with many points. I: Abelian and toric families. Journal of Algebra, 250(1):353-370.
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Let Nq(g) denote the maximal number of Fq-rational points on any curve of genus g over Fq. Ihara (for square q) and Serre (for general q) proved that lim supg→∞ Nq(g)/g > 0 for any fixed q. Here we prove limg→∞ Nq(g) = ∞. More precisely, we use abelian covers of ℙ1 to prove lim infg→∞ Nq(g)/(g/log g) > 0, and we use curves on toric surfaces to prove lim infg→∞ Nq(g)/g1/3 > 0; we also show that these results are the best possible that can be proved using these families of curves. © 2002 Elsevier Science (USA).
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||abelian covers; toric surfaces|
|Deposited On:||29 Nov 2010 16:27|
|Last Modified:||29 Nov 2013 15:40|
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