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

Dennis Eriksson (Institutionen för matematiska vetenskaper) ; Viktor Scharaschkin
Acta Arithmetica (0065-1036). Vol. 136 (2008), 2, p. 99–110.
[Artikel, refereegranskad vetenskaplig]

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 $\sha^1(A)$ 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.

Nyckelord: zero-cycles, Brauer-Manin obstruction



Denna post skapades 2016-12-07. Senast ändrad 2016-12-20.
CPL Pubid: 245929

 

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