On Manin's conjecture for a family of Châtelet surfaces

R de la Bretèche, TD Browning, E Peyre

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 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 contributionOn Manin's conjecture for a family of Châtelet surfaces
Original languageEnglish
Pages (from-to)297-343
Number of pages47
JournalAnnals of Mathematics
Volume175
Issue number1
DOIs
Publication statusPublished - 2012

Keywords

  • Chatelet surface, Fano variety, heights, Manin conjecture

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