STANDARD CONJECTURES FOR ABELIAN FOURFOLDS

Giuseppe Ancona (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Mathématiques [math]

Giuseppe Ancona. STANDARD CONJECTURES FOR ABELIAN FOURFOLDS. Inventiones Mathematicae, 2021, 223, pp.149-212. ⟨10.1007/s00222-020-00990-7⟩. ⟨hal-02933719⟩