Abstract
The object of this paper is to present the foundations of a theory of p-adic-valued height pairings
, 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.
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Mazur, B., Tate, J. (1983). Canonical Height Pairings via Biextensions. In: Artin, M., Tate, J. (eds) Arithmetic and Geometry. Progress in Mathematics, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-9284-3_9
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DOI: https://doi.org/10.1007/978-1-4757-9284-3_9
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