Principally polarizable isogeny classes of abelian surfaces over finite fields

• Autores: Everet W. Howe, Daniel Maisner, Enric Nart i Viñals , Christophe Ritzenthaler
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 1, 2008, págs. 121-127
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n1.a11
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• Resumen

  • Let $\calA$ be an isogeny class of abelian surfaces over $\fq$ with Weil polynomial $x^4 + ax^3 + bx^2 + aqx + q^2$. We show that $\calA$ does not contain a surface that has a principal polarization if and only if $a^2 - b = q$ and $b < 0$ and all prime divisors of $b$ are congruent to $1$ modulo~$3$.