Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2

Enric Nart; Christophe Ritzenthaler

doi:https://doi.org/10.1016/j.ffa.2007.09.006

Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2

Enric Nart, Christophe Ritzenthaler

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

We determine the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curves of genus 3 over F2n. The methods provide an explicit construction of supersingular curves of genus 3 with Jacobian in a prescribed isogeny class. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	676-702
Journal	Finite Fields and Their Applications
Volume	14
DOIs	https://doi.org/10.1016/j.ffa.2007.09.006
Publication status	Published - 1 Jul 2008

Keywords

Curve
Isogeny class
Jacobian
Maximal curves
Supersingular abelian threefold

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abstract = "We determine the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curves of genus 3 over F2n. The methods provide an explicit construction of supersingular curves of genus 3 with Jacobian in a prescribed isogeny class. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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author = "Enric Nart and Christophe Ritzenthaler",

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T1 - Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2

AU - Nart, Enric

AU - Ritzenthaler, Christophe

PY - 2008/7/1

Y1 - 2008/7/1

N2 - We determine the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curves of genus 3 over F2n. The methods provide an explicit construction of supersingular curves of genus 3 with Jacobian in a prescribed isogeny class. © 2007 Elsevier Inc. All rights reserved.

AB - We determine the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curves of genus 3 over F2n. The methods provide an explicit construction of supersingular curves of genus 3 with Jacobian in a prescribed isogeny class. © 2007 Elsevier Inc. All rights reserved.

KW - Curve

KW - Isogeny class

KW - Jacobian

KW - Maximal curves

KW - Supersingular abelian threefold

U2 - https://doi.org/10.1016/j.ffa.2007.09.006

DO - https://doi.org/10.1016/j.ffa.2007.09.006

M3 - Article

VL - 14

SP - 676

EP - 702

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

ER -