Geodesic
The number of varieties in a family which contain a rational point
Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2539-2588.

Voir la notice de l'article provenant de la source EMS Press

We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer–Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre’s problem.
DOI : 10.4171/jems/818
Classification : 11-XX, 14-XX
Mots-clés : Rational points, families of varieties, Brauer groups, toric varieties 
@article{JEMS_2018_20_10_a5,
     author = {Daniel Loughran},
     title = {The number of varieties in a family which contain a rational point},
     journal = {Journal of the European Mathematical Society},
     pages = {2539--2588},
     publisher = {mathdoc},
     volume = {20},
     number = {10},
     year = {2018},
     doi = {10.4171/jems/818},
     url = {https://geodesic-test.mathdoc.fr/articles/10.4171/jems/818/}
}
TY  - JOUR
AU  - Daniel Loughran
TI  - The number of varieties in a family which contain a rational point
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 2539
EP  - 2588
VL  - 20
IS  - 10
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.4171/jems/818/
DO  - 10.4171/jems/818
ID  - JEMS_2018_20_10_a5
ER  - 
%0 Journal Article
%A Daniel Loughran
%T The number of varieties in a family which contain a rational point
%J Journal of the European Mathematical Society
%D 2018
%P 2539-2588
%V 20
%N 10
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.4171/jems/818/
%R 10.4171/jems/818
%F JEMS_2018_20_10_a5
Daniel Loughran. The number of varieties in a family which contain a rational point. Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2539-2588. doi : 10.4171/jems/818. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/818/

Cité par Sources :