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arXiv · 1610.01932

N\'eron-Tate heights of cycles on jacobians

Robin de Jong
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Abstract

We develop a method to calculate the N\'eron-Tate height of tautological integral cycles on jacobians of curves defined over number fields. As examples we obtain closed expressions for the N\'eron-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 N\'eron-Tate height of a symmetric theta divisor.

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Robin de Jong. 2016-10-06. N\'eron-Tate heights of cycles on jacobians. https://doi.org/10.1090/jag%2F700

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