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.
KeywordsQuadratic Form Abelian Variety Number Field Finite Extension Divisor Class
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