We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology