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La conjecture de Manin pour certaines surfaces de Châtelet

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Destagnol K.

Acta Arithmetica

2016

tom 174

nr 1

31-97

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 deals with the last remaining case of Manin's conjecture for Châtelet surfaces with a = -1 and essentially settles Manin's conjecture for Châtelet surfaces with a < 0.

Ograniczanie wyników

1 Acta Arithmetica

1 Destagnol K.

1 2016

Wyniki wyszukiwania

La conjecture de Manin pour certaines surfaces de Châtelet