Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve
type: Item
instance of: scholarly article
title: Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve
zbMATH Open document ID: 0876.14022
author: Andreas Langer
published in: Documenta Mathematica
publication date: 1997-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/224150
full work available at URL: 03.html
review text: Summary: We extend the finiteness result on the \(p\)-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito [see \textit{A. Langer} and \textit{S. Saito}, ``Torsion zero-cycles on the self-product of a modular elliptic curve'', Duke Math. J. 85, No. 2, 315-357 (1996)] to primes \(p\) dividing the conductor. On the way we show the finiteness of the Selmer group associated to the symmetric square of the elliptic curve for those primes. The proof uses \(p\)-adic techniques, in particular the Fontaine-Jannsen conjecture proven by Kato and Tsuji.
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 19E15
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 1016571
zbMATH Keywords: torsion zero cycles
zbMATH Keywords: Selmer group of the symmetric square
zbMATH Keywords: Hyodo-Kato cohomology
zbMATH Keywords: selfproduct of a semistable elliptic curve
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1016571