Jacobians in isogeny classes of abelian surfaces over finite fields

Everett W. Howe; Enric Nart; Christophe Ritzenthaler

doi:10.5802/aif.2430

Jacobians in isogeny classes of abelian surfaces over finite fields

Everett W. Howe, Enric Nart, Christophe Ritzenthaler

Department of Mathematics

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

11 Citations (Scopus)

Abstract

We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus-2 curves over finite fields.

Original language	English
Pages (from-to)	239-289
Journal	Annales de l'Institut Fourier
Volume	59
Issue number	1
DOIs	https://doi.org/10.5802/aif.2430
Publication status	Published - 1 Jan 2009

Keywords

Abelian surface
Curve
Jacobian
Weil number
Weil polynomial
Zeta function

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title = "Jacobians in isogeny classes of abelian surfaces over finite fields",

abstract = "We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus-2 curves over finite fields.",

keywords = "Abelian surface, Curve, Jacobian, Weil number, Weil polynomial, Zeta function",

author = "Howe, {Everett W.} and Enric Nart and Christophe Ritzenthaler",

year = "2009",

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AU - Howe, Everett W.

AU - Nart, Enric

AU - Ritzenthaler, Christophe

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N2 - We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus-2 curves over finite fields.

AB - We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus-2 curves over finite fields.

KW - Abelian surface

KW - Curve

KW - Jacobian

KW - Weil number

KW - Weil polynomial

KW - Zeta function

U2 - 10.5802/aif.2430

DO - 10.5802/aif.2430

M3 - Article

VL - 59

SP - 239

EP - 289

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 1

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