Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2

Enric Nart, Christophe Ritzenthaler

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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 languageEnglish
Pages (from-to)676-702
JournalFinite Fields and Their Applications
Volume14
DOIs
Publication statusPublished - 1 Jul 2008

Keywords

  • Curve
  • Isogeny class
  • Jacobian
  • Maximal curves
  • Supersingular abelian threefold

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