The invariants of the Tate-Shafarevich group in a \({\mathbb{Z}}_ p\)- extension can be infinite
type: Item
instance of: scholarly article
title: The invariants of the Tate-Shafarevich group in a \({\mathbb{Z}}_ p\)- extension can be infinite
zbMATH Open document ID: 0581.14030
DOI: 10.1215/S0012-7094-85-05209-3
author: Gudrun Brattström
published in: Duke Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: In this paper, the author constructs examples which show that the Galois invariants of the p-primary subgroup of the Tate-Shafarevich group over a \({\mathbb{Z}}_ p\)-extension can be infinite. They are interesting in comparing with the conjecture on the finiteness of the Tate-Shafarevich group of an abelian variety over a number field.
Mathematics Subject Classification ID: 14K20
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 3929173
zbMATH Keywords: p-adic height pairing
zbMATH Keywords: Iwasawa power series
zbMATH Keywords: two-variable p-adic L- function
zbMATH Keywords: Galois invariants
zbMATH Keywords: finiteness of the Tate-Shafarevich group
reviewed by: Koji Katayama
MaRDI profile type: Publication
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full work available at URL: s0012-7094-85-05209-3
OpenAlex ID: W1555767650
description: scientific article; zbMATH DE number 3929173