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.
- Abelian surface
- Finite field
- Principal polarization
- Weil polynomial
Howe, E. W., Maisner, D., Nart, E., & Ritzenthaler, C. (2008). Principally polarizable isogeny classes of abelian surfaces over finite fields. Mathematical Research Letters, 15(1), 121-127. https://doi.org/10.4310/MRL.2008.v15.n1.a11