  Grothendieck's standard conjecture of Lefschetz type has two main forms: the
weak form $C$ and the strong form $B$. The weak form is known for varieties
over finite fields as a consequence of the proof of the Weil conjectures. This
suggests that the strong form of the conjecture in the same setting may be the
most accessible of the standard conjectures. Here, as an advertisement for the
conjecture, we explain some of its remarkable consequences.
