Néron models and the height jump divisor

Biesel, Owen; Holmes, David; de Jong, Robin

doi:10.1090/tran/7087

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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