On the integral Hodge conjecture for real abelian threefolds

Olivier de Gaay Fortman

On the integral Hodge conjecture for real abelian threefolds

Algebraic Geometry 2023-10-26 v2

Authors: Olivier de Gaay Fortman

Abstract

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.

Keywords

real abelian threefolds integral hodge conjecture real locus abelian surface elliptic curve jacobian modulo torsion

Cite

@article{arxiv.2211.04061,
  title  = {On the integral Hodge conjecture for real abelian threefolds},
  author = {Olivier de Gaay Fortman},
  journal= {arXiv preprint arXiv:2211.04061},
  year   = {2023}
}

Comments

36 pages. final version, to appear in Crelle's Journal. arXiv admin note: substantial text overlap with arXiv:2211.02710

On the integral Hodge conjecture for real abelian threefolds

Abstract

Keywords

Cite

Comments

Related papers