On Tate duality for Jacobian varieties.
type: Item
instance of: scholarly article
title: On Tate duality for Jacobian varieties.
zbMATH Open document ID: 1049.11129
DOI: 10.1016/S0022-314X(02)00067-7
author: Takao Yamazaki
published in: Journal of Number Theory
publication date: 2003-05-25T00:00:00Z
review text: 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 \(J\).
Mathematics Subject Classification ID: 11S25
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 11G10
zbMATH DE Number: 1915507
zbMATH Keywords: \(p\)-adic field
zbMATH Keywords: Galois cohomology
zbMATH Keywords: Abelian variety
zbMATH Keywords: wild ramification
zbMATH Keywords: Brauer group
reviewed by: Helmut Koch
MaRDI profile type: Publication
cites work: Q5525146
cites work: Q3739275
cites work: Néron Models
cites work: Kummer theory for abelian varieties over local fields
cites work: Q3203116
cites work: Duality theorems for curves over p-adic fields
cites work: Duality theorems for Néron models
cites work: Tate duality and wild ramification
cites work: Q3871006
cites work: Arithmetic on two dimensional local rings
cites work: Q5509718
cites work: Q3266818
cites work: Q4392681
cites work: On Swan conductors for Brauer groups of curves over local fields
full work available at URL: s0022-314x(02)00067-7
OpenAlex ID: W2042726685
description: scientific article; zbMATH DE number 1915507