On the Brauer-Manin obstruction for zero-cycles on curves

Eriksson, Dennis and Scharaschkin, Victor (2008) On the Brauer-Manin obstruction for zero-cycles on curves. Acta Arithmetica, 135 2: 99-110. doi:10.4064/aa135-2-1

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Author Eriksson, Dennis
Scharaschkin, Victor
Title On the Brauer-Manin obstruction for zero-cycles on curves
Journal name Acta Arithmetica   Check publisher's open access policy
ISSN 0065-1036
1730-6264
Publication date 2008-02-02
Sub-type Article (original research)
DOI 10.4064/aa135-2-1
Volume 135
Issue 2
Start page 99
End page 110
Total pages 12
Editor Jerzy Kaczorowski
Place of publication Warsaw, Poland
Publisher Polska Akademia Nauk, Instytut Matematyczny
Language eng
Subject 0101 Pure Mathematics
Formatted abstract
We wish to give a short elementary proof of S. Saito’s result that the Brauer-Manin obstruction for zero-cycles of degree 1 is the only one for curves, supposing the finiteness of the Tate-Shafarevich-group III1(A) of the Jacobian variety. In fact we show that we only need a conjecturally finite part of the Brauer-group for this obstruction to be the only one. We also comment on the situation in higher dimensions.
Keyword Albanese
Number theory
Algebraic geometry
Brauer-Manin obstruction
Q-Index Code C1
Q-Index Status Provisional Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
 
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Citation counts: TR Web of Science Citation Count  Cited 9 times in Thomson Reuters Web of Science Article | Citations
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