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Zbl 0743.14031
Jones, John W.
$p$-adic heights for semi-stable abelian varieties. (English)
[J] Compos. Math. 73, No.1, 31-56 (1990). ISSN 0010-437X; ISSN 1570-5846/e

This paper is concerned with the definition of an algebraic $p$-adic height pairing for abelian varieties over a number field with ordinary reduction at primes dividing $p$. The definition builds on work by {\it P. Schneider} [Invent. Math. 69, 401-409 (1982; Zbl 0509.14048)]. The novelty here is that this paper allows certain types of singular reductions for the abelian variety. The main techniques involved are computations involving Galois and flat cohomology groups. The paper goes on to prove that the height it defines is equivalent to an analytic height previously defined by Schneider.
[J.W.Jones (Austin)]

MSC 2000:: *14K15 Arithmetic ground fields (abelian varieties)
14G40 Arithmetic varieties and schemes
11R23 Iwasawa theory
14G25 Global ground fields

Keywords: algebraic $p$-adic height pairing for abelian varieties; singular reductions; cohomology groups

Citations: Zbl 0509.14048

Cited in: Zbl 0866.14027 Zbl 0823.11035

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