# On the Brauer-Manin obstruction for zero-cycles on curves Artikel i vetenskaplig tidskrift, 2008

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.

Brauer-Manin obstruction

zero-cycles

## Författare

#### Dennis Eriksson

Göteborgs universitet

Chalmers, Matematiska vetenskaper

#### Acta Arithmetica

0065-1036 (ISSN)

Vol. 136 2 99-110

Matematik

Geometri

#### Fundament

Grundläggande vetenskaper

2017-10-08