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arXiv · 2101.07506

The Walker Abel-Jacobi map descends

Jeff Achter·Sebastian Casalaina-Martin·Charles Vial
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Abstract

For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety, which admits a finite homomorphism to the Griffiths intermediate Jacobian. Recently Suzuki gave an alternate, Hodge-theoretic, construction of this Walker Abel-Jacobi map. We provide a third construction based on a general lifting property for surjective regular homomorphisms, and prove that the Walker Abel-Jacobi map descends canonically to any field of definition of the complex projective manifold. In addition, we determine the image of the l-adic Bloch map restricted to algebraically trivial cycle classes in terms of the coniveau filtration.

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Jeff Achter, Sebastian Casalaina-Martin, Charles Vial. 2021-01-19. The Walker Abel-Jacobi map descends. https://doi.org/10.1007/s00209-021-02833-4

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