Lefschetz classes of simple factors of Fermat Jacobian of prime degree   over finite fields
  We give a necessary and sufficient condition in terms of a matrix for which all Tate classes are Lefschetz for simple abelian varieties over an algebraic closure of a finite field. As an application, we prove under an assumption that all Tate classes are Lefschetz for simple factors of Fermat Jacobian of prime degree. 
Rin Sugiyama
math.NT math.AG