On the BrauerManin obstruction for zerocycles on curves
Abstract
We wish to give a short elementary proof of S. Saito's result that the BrauerManin obstruction for zerocycles of degree 1 is the only one for curves, supposing the finiteness of the TateShafarevichgroup $\sha^1(A)$ of the Jacobian variety. In fact we show that we only need a conjecturally finite part of the Brauergroup for this obstruction to be the only one. We also comment on the situation in higher dimensions
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2006
 DOI:
 10.48550/arXiv.math/0602355
 arXiv:
 arXiv:math/0602355
 Bibcode:
 2006math......2355E
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G30;
 16K50;
 14L10
 EPrint:
 12 pages