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2016 Progress concerning the local-global principle for zero-cycles on algebraic varieties
Yongqi Liang
Rocky Mountain J. Math. 46(4): 1293-1308 (2016). DOI: 10.1216/RMJ-2016-46-4-1293


We consider zero-cycles on algebraic varieties defined over number fields. The Hasse principle and weak approximation property are obstructed by the Brauer group of the variety and it is conjectured to be the only obstruction for all proper smooth varieties by Colliot-Th\'el\`ene, Sansuc, Kato and Saito. We summarize the progress related to this conjecture, particularly for higher dimensional varieties such as fibrations and homogeneous varieties.


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Yongqi Liang. "Progress concerning the local-global principle for zero-cycles on algebraic varieties." Rocky Mountain J. Math. 46 (4) 1293 - 1308, 2016.


Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1358.11073
MathSciNet: MR3563183
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1293

Primary: 11G35 , 14C25 , 14G25

Keywords: Brauer and Manin's obstruction , Hasse principle , weak approximation , zero-cycles

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 4 • 2016
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