Geodesic
On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
Jörg Jahnel1 ; Damaris Schindler2
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.

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

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 
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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. http://geodesic.mathdoc.fr/articles/10.4064/aa8123-8-2016/

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