Principally polarizable isogeny classes of abelian surfaces over finite fields

Details Principally polarizable isogeny classes of abelian surfaces over finite fields Principally polarizable isogeny classes of abelian surfaces over finite fields

2006-02-28

arxiv.org/abs/math/0602650v1

Math. Res. Lett. 15 (2008) 121-127

Mathematics

Number Theory

Scientific paper

Let A be an isogeny class of abelian surfaces over F_q with Weil polynomial x^4 + ax^3 + bx^2 + aqx + q^2. We show that A 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. 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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