Canonical Height Pairings via Biextensions

  • Barry Mazur
  • John Tate
Part of the Progress in Mathematics book series (PM, volume 35)


The object of this paper is to present the foundations of a theory of p-adic-valued height pairings
$$A\left( K \right) \times A'\left( K \right) \to {Q_p}$$
, where Λ is a abelian variety over a global field K, and A′ is its dual. We say “pairings” in the plural because, in contrast to the classical theory of ℝ-valued) canonical height, there may be many canonical p-adic valued pairings: as we explain in § 4, up to nontrivial scalar multiple, they are in one-to-one correspondence with ℤ p -extensions L/K whose ramified primes are finite in number and are primes of ordinary reduction (1.1) for A.


Elliptic Curf Abelian Variety Group Scheme Finite Index Algebraic Space 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Barry Mazur
    • 1
  • John Tate
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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