Geodesic
On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
Jörg Jahnel 1   ; Damaris Schindler 2
1 Department Mathematik Universität Siegen Walter-Flex-Str. 3 D-57068 Siegen, Germany
2 Mathematisch Instituut Universiteit Utrecht Budapestlaan 6 NL-3584 CD Utrecht, The Netherlands
Acta Arithmetica, Tome 176 (2016) no. 4, pp. 301-319 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We show that for every integer $1 \leq d \leq 4$ and every finite set $S$ of places, there exists a degree-$d$ del Pezzo surface $X$ over $\mathbb Q$ such that $\operatorname{Br}(X)/\!\operatorname{Br}(\mathbb Q) \cong \mathbb Z/2\mathbb Z$ and the nontrivial Brauer class has a nonconstant local evaluation exactly at the places in $S$. For $d = 4$, we prove that in all cases except $S = \{\infty\}$, this surface may be chosen diagonalisably over $\mathbb Q$.
DOI : 10.4064/aa8123-8-2016
Keywords: every integer leq leq every finite set places there exists degree d del pezzo surface mathbb operatorname operatorname mathbb cong mathbb mathbb nontrivial brauer class has nonconstant local evaluation exactly places prove cases except infty surface may chosen diagonalisably nbsp mathbb

Jörg Jahnel  1   ; Damaris Schindler  2

1 Department Mathematik Universität Siegen Walter-Flex-Str. 3 D-57068 Siegen, Germany
2 Mathematisch Instituut Universiteit Utrecht Budapestlaan 6 NL-3584 CD Utrecht, The Netherlands 
@article{10_4064_aa8123_8_2016,
     author = {J\"org Jahnel and Damaris Schindler},
     title = {On the {Brauer{\textendash}Manin} obstruction for degree-four del {Pezzo} surfaces},
     journal = {Acta Arithmetica},
     pages = {301--319},
     year = {2016},
     volume = {176},
     number = {4},
     doi = {10.4064/aa8123-8-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8123-8-2016/}
}
TY  - JOUR
AU  - Jörg Jahnel
AU  - Damaris Schindler
TI  - On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
JO  - Acta Arithmetica
PY  - 2016
SP  - 301
EP  - 319
VL  - 176
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8123-8-2016/
DO  - 10.4064/aa8123-8-2016
LA  - en
ID  - 10_4064_aa8123_8_2016
ER  - 
%0 Journal Article
%A Jörg Jahnel
%A Damaris Schindler
%T On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
%J Acta Arithmetica
%D 2016
%P 301-319
%V 176
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8123-8-2016/
%R 10.4064/aa8123-8-2016
%G en
%F 10_4064_aa8123_8_2016
Jörg Jahnel; Damaris Schindler. On the Brauer–Manin obstruction for degree-four del Pezzo surfaces. Acta Arithmetica, Tome 176 (2016) no. 4, pp. 301-319. doi: 10.4064/aa8123-8-2016

Cité par Sources :