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DISTINGUISHED MODELS OF INTERMEDIATE JACOBIANS
Published online by Cambridge University Press: 08 June 2018
Abstract
We show that the image of the Abel–Jacobi map admits functorially a model over the field of definition, with the property that the Abel–Jacobi map is equivariant with respect to this model. The cohomology of this abelian variety over the base field is isomorphic as a Galois representation to the deepest part of the coniveau filtration of the cohomology of the projective variety. Moreover, we show that this model over the base field is dominated by the Albanese variety of a product of components of the Hilbert scheme of the projective variety, and thus we answer a question of Mazur. We also recover a result of Deligne on complete intersections of Hodge level 1.
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- Research Article
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- © Cambridge University Press 2018
Footnotes
The first author was partially supported by grants from the NSA (H98230-14-1-0161, H98230-15-1-0247 and H98230-16-1-0046). The second author was partially supported by a Simons Foundation Collaboration Grant for Mathematicians (317572) and NSA grant H98230-16-1-0053. The third author was supported by EPSRC Early Career Fellowship EP/K005545/1.
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