On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
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 $\mathbb Q$.
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
@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},
publisher = {mathdoc},
volume = {176},
number = {4},
year = {2016},
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 PB - mathdoc 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 -
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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
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