La conjecture de Manin pour certaines surfaces de Châtelet
Following the line of attack of La Bretèche, Browning and Peyre, we prove Manin's conjecture in its strong form conjectured by Peyre for a family of Châtelet surfaces which are defined as minimal proper smooth models of affine surfaces of the form Y² - aZ² = F(X,1), where a = -1, F ∈ ℤ[x₁,x₂] is a polynomial of degree 4 whose factorisation into irreducibles contains two non-proportional linear factors and a quadratic factor which is irreducible over ℚ [i]. This result...