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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lewis, James D. 2016. Lectures on Hodge Theory and Algebraic Cycles. Communications in Mathematics and Statistics, Vol. 4, Issue. 2, p. 93.


    Schnell, Christian 2012. Complex analytic Néron models for arbitrary families of intermediate Jacobians. Inventiones mathematicae, Vol. 188, Issue. 1, p. 1.


    Saito, Morihiko and Schnell, Christian 2011. A variant of Néron models over curves. Manuscripta Mathematica, Vol. 134, Issue. 3-4, p. 359.


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Néron models and limits of Abel–Jacobi mappings

  • Mark Green (a1), Phillip Griffiths (a2) and Matt Kerr (a3)
  • DOI: http://dx.doi.org/10.1112/S0010437X09004400
  • Published online: 02 February 2010
Abstract
Abstract

We show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on motivic cohomology of the singular fibre, hence via regulators on K-groups of its substrata. Two examples are worked out in detail, for families of 1-cycles on CY and abelian 3-folds, where this produces interesting arithmetic constraints on such limits. We also show how to compute the finite ‘singularity group’ in the geometric setting.

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