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arXiv · 1503.08292

On the Brauer-Manin obstruction for degree four del Pezzo surfaces

Jörg Jahnel·Damaris Schindler
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Abstract

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 ${\rm Br}(X)/{\rm Br}({\mathbb Q}) \cong {\mathbb Z}/2{\mathbb Z}$ and the Brauer-Manin obstruction works exactly at the places in $S$. For $d = 4$, we prove that in all cases, with the exception of $S = \{\infty\}$, this surface may be chosen diagonalizably over ${\mathbb Q}$.

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Jörg Jahnel, Damaris Schindler. 2015-03-28. On the Brauer-Manin obstruction for degree four del Pezzo surfaces. https://arxiv.org/abs/1503.08292

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