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Zeta Functions of Supersingular Curves of Genus 2

Published online by Cambridge University Press:  20 November 2018

Daniel Maisner  and
Enric Nart
Daniel Maisner
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spainemail: danielm@mat.uab.es, nart@mat.uab.es
Enric Nart
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spainemail: danielm@mat.uab.es, nart@mat.uab.es
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Abstract

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We determine which isogeny classes of supersingular abelian surfaces over a finite field $k$ of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to $k$-isomorphism, leading to the same zeta function.

Keywords

11G2014G1511G10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 2 , 01 April 2007 , pp. 372 - 392
Copyright
Copyright © Canadian Mathematical Society 2007

References

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