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Néron models and the height jump divisor


Authors: Owen Biesel, David Holmes and Robin de Jong
Journal: Trans. Amer. Math. Soc. 369 (2017), 8685-8723
MSC (2010): Primary 14H10; Secondary 11G50, 14G40, 14K15
DOI: https://doi.org/10.1090/tran/7087
Published electronically: June 27, 2017
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Abstract: We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the height jump for families of semistable curves using labelled reduction graphs. With these techniques we prove a conjecture of Hain on the effectivity of the height jump, and also give a new proof of a theorem of Tate, Silverman and Green on the variation of heights in families of abelian varieties.


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Additional Information

Owen Biesel
Affiliation: Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email: bieselod@math.leidenuniv.nl

David Holmes
Affiliation: Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email: holmesdst@math.leidenuniv.nl

Robin de Jong
Affiliation: Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email: rdejong@math.leidenuniv.nl

DOI: https://doi.org/10.1090/tran/7087
Keywords: Canonical height, Deligne pairing, dual graph, effective resistance, Green's function, height jump divisor, labelled graph, N\'eron model, resistive network
Received by editor(s): January 30, 2015
Received by editor(s) in revised form: February 15, 2016
Published electronically: June 27, 2017
Article copyright: © Copyright 2017 by the authors

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