Abstract
I can now answer your question1 concerning a “geometric” or “physical” description of the 2-extension class assigned to an algebraic cycle mapping to zero under the Abel-Jacobi map. I shall describe everything in the ℓ-adic setting; similar results can be stated for every reasonable cohomology theory (as in 11.5 of [1] Jannsen, U.: Mixed motives and algebraic K-theory, Habilitationsschrift Regensburg 19882).
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Gordon, B.B., Lewis, J.D., Müller-Stach, S., Saito, S., Yui, N. (2000). Letter from Jannsen to Gross on higher Abel-Jacobi maps. In: Gordon, B.B., Lewis, J.D., Müller-Stach, S., Saito, S., Yui, N. (eds) The Arithmetic and Geometry of Algebraic Cycles. NATO Science Series, vol 548. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4098-0_8
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DOI: https://doi.org/10.1007/978-94-011-4098-0_8
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