On Manin's conjecture for a family of Châtelet surfaces

R de la Bretèche; TD Browning; E Peyre

doi:10.4007/annals.2012.175.1.8

On Manin's conjecture for a family of Châtelet surfaces

R de la Bretèche
, TD Browning
, E Peyre

Research output: Contribution to journal › Article (Academic Journal) › peer-review

27 Citations (Scopus)

Abstract

The Manin conjecture is established for Châtelet surfaces over Q arising as minimal proper smooth models of the surface Y2+Z2=f(X) in A3Q, where f∈Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation

Translated title of the contribution	On Manin's conjecture for a family of Châtelet surfaces
Original language	English
Pages (from-to)	297-343
Number of pages	47
Journal	Annals of Mathematics
Volume	175
Issue number	1
DOIs	https://doi.org/10.4007/annals.2012.175.1.8
Publication status	Published - 2012

Keywords

Chatelet surface, Fano variety, heights, Manin conjecture

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10.4007/annals.2012.175.1.8

http://annals.math.princeton.edu/2012/175-1/p08

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DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY
Browning, T. D. (Principal Investigator)
1/09/07 → 1/04/13
Project: Research

Cite this

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title = "On Manin's conjecture for a family of Ch{\^a}telet surfaces",

abstract = "The Manin conjecture is established for Ch{\^a}telet surfaces over Q arising as minimal proper smooth models of the surface Y2+Z2=f(X) in A3Q, where f∈Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation",

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AU - de la Bretèche, R

AU - Browning, TD

AU - Peyre, E

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N2 - The Manin conjecture is established for Châtelet surfaces over Q arising as minimal proper smooth models of the surface Y2+Z2=f(X) in A3Q, where f∈Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation

AB - The Manin conjecture is established for Châtelet surfaces over Q arising as minimal proper smooth models of the surface Y2+Z2=f(X) in A3Q, where f∈Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation

KW - Chatelet surface, Fano variety, heights, Manin conjecture

U2 - 10.4007/annals.2012.175.1.8

DO - 10.4007/annals.2012.175.1.8

M3 - Article (Academic Journal)

SN - 0003-486X

VL - 175

SP - 297

EP - 343

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 1

ER -

On Manin's conjecture for a family of Châtelet surfaces

Abstract

Keywords

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DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY

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