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arXiv · 1806.03216

Standard conjectures for abelian fourfolds

Giuseppe Ancona
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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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Giuseppe Ancona. 2018-06-08. Standard conjectures for abelian fourfolds. https://doi.org/10.1007/s00222-020-00990-7

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