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arXiv · 1711.01882

Description de torseurs quasi-versels pour une famille de surfaces fibrées en coniques

Kevin Destagnol
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Abstract

Generalising work of La Bretèche, Browning and Peyre and of the author, we describe the geometry required by Manin's principle and Peyre's conjecture for a family of conic bundle surfaces containing Châtelet surfaces. These surfaces $S_{a,F}$ are the conic bundle surfaces obtained as smooth minimal proper model of $$ Y^2-aZ^2=F(X,1) $$ with $a \in \mathbf{Z}$ squarefree and $F \in \mathbf{Z}[x_1,x_2]$ a binary form of \textit{even} degree $n$ without repeated roots and whose irreducible factors over $\mathbf{Q}$ remain irreducible over $\mathbf{Q}\left( \sqrt{a} \right)$.

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Kevin Destagnol. 2018-01-29. Description de torseurs quasi-versels pour une famille de surfaces fibrées en coniques. https://arxiv.org/abs/1711.01882

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