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

Access to Document

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

Cite this

@article{03db20b2c3f34b37b00b38e9b3823d4d,

title = "Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2",

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.",

keywords = "Curve, Isogeny class, Jacobian, Maximal curves, Supersingular abelian threefold",

author = "Enric Nart and Christophe Ritzenthaler",

year = "2008",

month = jul,

day = "1",

doi = "https://doi.org/10.1016/j.ffa.2007.09.006",

language = "English",

volume = "14",

pages = "676--702",

journal = "Finite Fields and Their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

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 -

Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2

Abstract

Keywords

Access to Document

Fingerprint

Cite this