Principally polarizable isogeny classes of abelian surfaces over finite fields
Abstract
Let A be an isogeny class of abelian surfaces over Fq with Weil polynomial x4 + ax3 + bx2 + aqx + q2. We show that A does not contain a surface that has a principal polarization if and only if a2 - b = q and b < 0 and all prime divisors of b are congruent to 1 modulo 3. We use this result in a forthcoming paper in which we determine which isogeny classes of abelian surfaces over finite fields contain Jacobians.
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