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Heights on Abelian Varieties

In: Fundamentals of Diophantine Geometry

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  • Serge Lang

    (Yale University, Department of Mathematics)

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.

Suggested Citation

  • Serge Lang, 1983. "Heights on Abelian Varieties," Springer Books, in: Fundamentals of Diophantine Geometry, chapter 0, pages 95-137, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-1810-2_5
    DOI: 10.1007/978-1-4757-1810-2_5
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