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STANDARD CONJECTURES FOR ABELIAN FOURFOLDS

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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https://hal.archives-ouvertes.fr/hal-02933719
Contributor : Giuseppe Ancona <>
Submitted on : Tuesday, September 8, 2020 - 5:08:51 PM
Last modification on : Tuesday, September 15, 2020 - 3:36:49 AM

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Giuseppe Ancona. STANDARD CONJECTURES FOR ABELIAN FOURFOLDS. Inventiones Mathematicae, Springer Verlag, In press, ⟨10.1007/s00222-020-00990-7⟩. ⟨hal-02933719⟩

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