The Walker Abel-Jacobi map descends
Autor: | Charles Vial, Jeffrey D. Achter, Sebastian Casalaina-Martin |
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Jazyk: | angličtina |
Rok vydání: | 2022 |
Předmět: |
Abelian variety
Pure mathematics Intermediate Jacobian General Mathematics Manifold Image (mathematics) Surjective function Field of definition Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry FOS: Mathematics Filtration (mathematics) Homomorphism Algebraic Geometry (math.AG) Mathematics |
Popis: | 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. 17 pages |
Databáze: | OpenAIRE |
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