La conjecture de Manin pour certaines surfaces de Châtelet

Kevin Destagnol

Acta Arithmetica (2016)

  • Volume: 174, Issue: 1, page 31-97
  • ISSN: 0065-1036

Abstract

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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.

How to cite

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Kevin Destagnol. "La conjecture de Manin pour certaines surfaces de Châtelet." Acta Arithmetica 174.1 (2016): 31-97. <http://eudml.org/doc/286559>.

@article{KevinDestagnol2016,
author = {Kevin Destagnol},
journal = {Acta Arithmetica},
keywords = {manin's conjecture; peyre's constant; chatelet surfaces; number of representations as sum of two squares; descent method; torsors; counting rational points on algebraic varieties},
language = {fre},
number = {1},
pages = {31-97},
title = {La conjecture de Manin pour certaines surfaces de Châtelet},
url = {http://eudml.org/doc/286559},
volume = {174},
year = {2016},
}

TY - JOUR
AU - Kevin Destagnol
TI - La conjecture de Manin pour certaines surfaces de Châtelet
JO - Acta Arithmetica
PY - 2016
VL - 174
IS - 1
SP - 31
EP - 97
LA - fre
KW - manin's conjecture; peyre's constant; chatelet surfaces; number of representations as sum of two squares; descent method; torsors; counting rational points on algebraic varieties
UR - http://eudml.org/doc/286559
ER -

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