Zarhin trick

In mathematics, the Zarhin trick is a method for eliminating the polarization of abelian varieties A by observing that the abelian variety A⁴ × Â⁴ is principally polarized. The method was introduced by Zarhin (1974) in his proof of the Tate conjecture over global fields of positive characteristic.

References

• Zarhin, Ju. G. (1974), "A remark on endomorphisms of abelian varieties over function fields of finite characteristic", Mathematics of the USSR-Izvestiya, 8 (3): 477–480, doi:10.1070/IM1974v008n03ABEH002115, ISSN 0373-2436, MR 0354689