On Mumford’s Uniformization and Neron Models of Jacobians of Semistable Curves over Complete Rings

Crystalline subrepresentations and Neron models

Mathematical Research Letters ◽

10.4310/mrl.2000.v7.n5.a6 ◽

2000 ◽

Vol 7 (5) ◽

pp. 605-614

Author(s):

Minhyong Kim ◽

Susan H. Marshall

Keyword(s):

Neron Models ◽

Néron Models

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Néron models

European Journal of Mathematics ◽

10.1007/s40879-017-0134-8 ◽

2017 ◽

Vol 3 (2) ◽

pp. 171-198

Author(s):

Dino Lorenzini

Keyword(s):

Neron Models ◽

Néron Models

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Néron models and limits of Abel–Jacobi mappings

Compositio Mathematica ◽

10.1112/s0010437x09004400 ◽

2010 ◽

Vol 146 (2) ◽

pp. 288-366 ◽

Cited By ~ 6

Author(s):

Mark Green ◽

Phillip Griffiths ◽

Matt Kerr

Keyword(s):

Normal Function ◽

Motivic Cohomology ◽

Normal Functions ◽

Geometric Setting ◽

Neron Models ◽

A Finite Group ◽

Intermediate Jacobian ◽

Néron Models ◽

Singular Fibre ◽

Finite Singularity

AbstractWe 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 onK-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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