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Néron Functions on Abelian Varieties

In: Fundamentals of Diophantine Geometry

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  • Serge Lang

    (Yale University, Department of Mathematics)

Abstract

On an arbitrary variety, a Weil function associated to a divisor is defined only up to a bounded function. On abelian varieties, Néron showed how to define a function more canonically, up to a constant function. This chapter develops Néron’s results, but in §1 we shall prove existence by a method due to Tate, which is much simpler than Néron’s original construction, and is the analogue of Tate’s limit procedure for the height.

Suggested Citation

  • Serge Lang, 1983. "Néron Functions on Abelian Varieties," Springer Books, in: Fundamentals of Diophantine Geometry, chapter 0, pages 266-295, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-1810-2_11
    DOI: 10.1007/978-1-4757-1810-2_11
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