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Pré-Publication, Document De Travail Année : 2022

On the integral Hodge conjecture for real abelian threefolds

Résumé

We prove the real integral Hodge conjecture for several classes of real abelian threefolds. For instance, we prove the property for real abelian threefolds $A$ whose real locus $A(\mathbb R)$ is connected, and for real abelian threefolds $A$ which are a product $A = B \times E$ of an abelian surface $B$ and an elliptic curve $E$ with connected real locus $E(\mathbb R)$. Moreover, we show that every real abelian threefold satisfies the real integral Hodge conjecture modulo torsion, and reduce the general case to the Jacobian case.
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Dates et versions

hal-04003085 , version 1 (23-02-2023)

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Olivier de Gaay Fortman. On the integral Hodge conjecture for real abelian threefolds. 2023. ⟨hal-04003085⟩
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