Mathematical Research Letters
Volume 15 (2008)
Principally polarizable isogeny classes of abelian surfaces over finite fields
Pages: 121 – 127
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~$3$.
Published 1 January 2008