La conjecture de Manin pour certaines surfaces de Châtelet

• Autorzy: Kevin Destagnol
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11D45: Counting solutions of Diophantine equations
• 11D57: Multiplicative and norm form equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 174
• Numer: 1
• Strony: 31-97

Daty

wydano

2016

Twórcy

autor

Kevin Destagnol

• Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, Université Paris Diderot-Paris 7, Case postale 6052, Bâtiment Sophie Germain, 75205 Paris Cedex 13, France

Identyfikatory

DOI

10.4064/aa8312-2-2016