1Department Mathematik Universität Siegen Walter-Flex-Str. 3 D-57068 Siegen, Germany 2Mathematisch Instituut Universiteit Utrecht Budapestlaan 6 NL-3584 CD Utrecht, The Netherlands
Acta Arithmetica, Tome 176 (2016) no. 4, pp. 301-319
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 $\mathbb Q$.
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
Affiliations des auteurs :
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/}
}
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AU - Jörg Jahnel
AU - Damaris Schindler
TI - On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
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%J Acta Arithmetica
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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
