Abstract
Néron at the Edinburgh International Congress had conjectured that the (logarithmic) height on an abelian variety differed from a quadratic function by a bounded function. He proved this in [Ne 3], as well as proving an analogous statement for local components for the height. Tate showed that a direct argument applied to the global height could be used, by-passing the local considerations. We shall give Tate’s argument in this chapter, as well as a few consequences.
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© 1983 Springer Science+Business Media New York
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Lang, S. (1983). Heights on Abelian Varieties. In: Fundamentals of Diophantine Geometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1810-2_5
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DOI: https://doi.org/10.1007/978-1-4757-1810-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2818-4
Online ISBN: 978-1-4757-1810-2
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