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

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 $$Y^2-a{Z}^2=F(X,1)$$ 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 $\mathbf{Q}\left(\sqrt{a}\right)$.

In French, minor revisions. Comments welcome!

Cited by in corpus (1)

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