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Standard conjectures for abelian fourfolds (1806.03216v3)
Published 8 Jun 2018 in math.AG and math.NT
Abstract: 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.
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