Geodesic
On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields
Kento Yamamoto1
1 Department of Mathematics Chuo University 1-13-27 Kasuga, Bunkyo-Ku Tokyo 112-8551, Japan
Acta Arithmetica, Tome 181 (2017) no. 1, pp. 75-84.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that the degree-zero part of the Chow group of $0$-cycles on some diagonal cubic surface over a 3-adic field is generated by the classes of rational points. In the proof of the main result, we will construct explicit generators over the cubic unramified scalar extension. A key point is to check that such cycles have non-zero values under the Brauer–Manin pairing. We will use the Hilbert symbol to compute them.
DOI : 10.4064/aa8646-5-2017
Keywords: degree zero part chow group cycles diagonal cubic surface adic field generated classes rational points proof main result construct explicit generators cubic unramified scalar extension key point check cycles have non zero values under brauer manin pairing hilbert symbol compute

Kento Yamamoto 1

1 Department of Mathematics Chuo University 1-13-27 Kasuga, Bunkyo-Ku Tokyo 112-8551, Japan 
@article{10_4064_aa8646_5_2017,
     author = {Kento Yamamoto},
     title = {On generators of the {Chow} group of 0-cycles on diagonal cubic surfaces over 3-adic fields},
     journal = {Acta Arithmetica},
     pages = {75--84},
     publisher = {mathdoc},
     volume = {181},
     number = {1},
     year = {2017},
     doi = {10.4064/aa8646-5-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8646-5-2017/}
}
TY  - JOUR
AU  - Kento Yamamoto
TI  - On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields
JO  - Acta Arithmetica
PY  - 2017
SP  - 75
EP  - 84
VL  - 181
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8646-5-2017/
DO  - 10.4064/aa8646-5-2017
LA  - en
ID  - 10_4064_aa8646_5_2017
ER  - 
%0 Journal Article
%A Kento Yamamoto
%T On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields
%J Acta Arithmetica
%D 2017
%P 75-84
%V 181
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8646-5-2017/
%R 10.4064/aa8646-5-2017
%G en
%F 10_4064_aa8646_5_2017
Kento Yamamoto. On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields. Acta Arithmetica, Tome 181 (2017) no. 1, pp. 75-84. doi : 10.4064/aa8646-5-2017. http://geodesic.mathdoc.fr/articles/10.4064/aa8646-5-2017/

Cité par Sources :