Néron-Tate heights of cycles on jacobians

de Jong, Robin

doi:10.1090/jag/700

Author: Robin de Jong
Journal: J. Algebraic Geom. 27 (2018), 339-381
DOI: https://doi.org/10.1090/jag/700
Published electronically: January 25, 2018
MathSciNet review: 3764279
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Abstract | References | Additional Information

Abstract: We develop a method to calculate the Néron-Tate height of tautological integral cycles on jacobians of curves defined over number fields. As examples we obtain closed expressions for the Néron-Tate height of the difference surface, the Abel-Jacobi images of the square of the curve, and of any symmetric theta divisor. As applications we obtain a new effective positive lower bound for the essential minimum of any Abel-Jacobi image of the curve and a proof, in the case of jacobians, of a formula proposed by Autissier relating the Faltings height of a principally polarized abelian variety with the Néron-Tate height of a symmetric theta divisor.

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Additional Information

Robin de Jong
Affiliation: Mathematical Institute, Leiden University, P. O. Box 9512, 2300 RA Leiden, The Netherlands
MR Author ID: 723243
Email: rdejong@math.leidenuniv.nl

Received by editor(s): October 14, 2016
Received by editor(s) in revised form: January 22, 2017
Published electronically: January 25, 2018
Article copyright: © Copyright 2018 University Press, Inc.