  Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type
for A. By combining this result with a theorem of Clozel we deduce that
numerical equivalence on A coincides with l-adic homological equivalence on A
for infinitely many l. The approach consists in reformulating this question
into a p-adic problem and then using p-adic Hodge Theory to solve it.
