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

Research paper by Dennis Eriksson, Victor Scharaschkin

Indexed on: 16 Feb '06Published on: 16 Feb '06Published in: Mathematics - Number Theory



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 $\sha^1(A)$ 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