Heights on Abelian Varieties

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter 5 in Fundamentals of Diophantine Geometry, 1983, pp 95-137 from Springer

Abstract: 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.

Keywords: Quadratic Form; Abelian Variety; Number Field; Finite Extension; Divisor Class (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4757-1810-2_5

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