Principally polarizable isogeny classes of abelian surfaces over finite fields

Christophe Ritzenthaler; Enric Nart; Everett W. Howe; Daniel Maisner

doi:10.4310/MRL.2008.v15.n1.a11

Principally polarizable isogeny classes of abelian surfaces over finite fields

Christophe Ritzenthaler, Enric Nart, Everett W. Howe, Daniel Maisner

Departament de Matemàtiques

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Resum

Let A be an isogeny class of abelian surfaces over double-struck F signq with Weil polynomial x4 +ax3 + bx 2 + aqx + q2. We show that .4 does not contain a surface that has a principal polarization if and only if a2 -b = q and 6 < 0 and all prime divisors of b are congruent to 1 modulo 3. © International Press 2008.

Idioma original	Anglès
Pàgines (de-a)	121-127
Revista	Mathematical Research Letters
Volum	15
Número	1
DOIs	https://doi.org/10.4310/MRL.2008.v15.n1.a11
Estat de la publicació	Publicada - 1 de gen. 2008

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title = "Principally polarizable isogeny classes of abelian surfaces over finite fields",

abstract = "Let A be an isogeny class of abelian surfaces over double-struck F signq with Weil polynomial x4 +ax3 + bx 2 + aqx + q2. We show that .4 does not contain a surface that has a principal polarization if and only if a2 -b = q and 6 < 0 and all prime divisors of b are congruent to 1 modulo 3. {\textcopyright} International Press 2008.",

keywords = "Finite field, Abelian surface, Weil polynomial, Principal polarization",

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

year = "2008",

month = jan,

day = "1",

doi = "10.4310/MRL.2008.v15.n1.a11",

language = "English",

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pages = "121--127",

journal = "Mathematical Research Letters",

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AU - Ritzenthaler, Christophe

AU - Nart, Enric

AU - Howe, Everett W.

AU - Maisner, Daniel

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Let A be an isogeny class of abelian surfaces over double-struck F signq with Weil polynomial x4 +ax3 + bx 2 + aqx + q2. We show that .4 does not contain a surface that has a principal polarization if and only if a2 -b = q and 6 < 0 and all prime divisors of b are congruent to 1 modulo 3. © International Press 2008.

AB - Let A be an isogeny class of abelian surfaces over double-struck F signq with Weil polynomial x4 +ax3 + bx 2 + aqx + q2. We show that .4 does not contain a surface that has a principal polarization if and only if a2 -b = q and 6 < 0 and all prime divisors of b are congruent to 1 modulo 3. © International Press 2008.

KW - Finite field

KW - Abelian surface

KW - Weil polynomial

KW - Principal polarization

UR - https://dialnet.unirioja.es/servlet/articulo?codigo=2971421

U2 - 10.4310/MRL.2008.v15.n1.a11

DO - 10.4310/MRL.2008.v15.n1.a11

M3 - Article

SN - 1073-2780

VL - 15

SP - 121

EP - 127

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 1

ER -

Principally polarizable isogeny classes of abelian surfaces over finite fields

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