BOUND ON THE NUMBER OF RATIONAL POINTS ON CURVES ON HIRZEBRUCH SURFACES OVER FINITE FIELDS

Abstract : This paper gives a bound on the number of rational points on an absolutely irreducible curve C lying on a minimal toric surface X. This upper bound improves pre-existing ones if C has large genus. The strategy consists in finding another curve that intersects C with good multiplicity at its rational points outside some well-handled closed set. Finding such a curve relies on an extension of K.O. StöhrSt¨Stöhr and F.J. Voloch's idea for plane curves to the toric framework based on homogenization.
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https://hal.archives-ouvertes.fr/hal-02071479
Contributor : Jade Nardi <>
Submitted on : Monday, March 18, 2019 - 3:55:35 PM
Last modification on : Friday, October 11, 2019 - 8:22:43 PM
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  • HAL Id : hal-02071479, version 1

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Jade Nardi. BOUND ON THE NUMBER OF RATIONAL POINTS ON CURVES ON HIRZEBRUCH SURFACES OVER FINITE FIELDS. 2019. ⟨hal-02071479⟩

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