On Tate duality for Jacobian varieties. (English) Zbl 1049.11129

Yamazaki, Takao

J. Number Theory 99, No. 2, 298-306 (2003).

Let \(k\) be a \(p\)-adic number field and let \(A(k)\) be an abelian variety over \(k\) with dual \(A^t(k)\). The author studies Tate’s pairing \(A(k)\times H^1(k,A^t(k))\to \mathbb Q/\mathbb Z\) in the case that \(A=J\) is the Jacobian of a curve. He gives a description of the annihilator of \(U^nj(k)\) with respect to the Tate pairing, where \(\{U^nJ(k) | n=0,1,\dots\}\) is a filtration of \(J(k)\) given by the Néron model of \(J\).

Reviewer: Helmut Koch (Berlin)

MSC:

11S25	Galois cohomology
14H40	Jacobians, Prym varieties
14G20	Local ground fields in algebraic geometry
11G10	Abelian varieties of dimension \(> 1\)

Keywords:

\(p\)-adic field; Galois cohomology; Abelian variety; wild ramification; Brauer group

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