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Zeta Functions of Supersingular Curves of Genus 2
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2007
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