Rational points on pencils of conics and quadrics with many degenerate fibres

T. D. Browning; L. Matthiesen; A. N. Skorobogatov

doi:10.4007/annals.2014.180.1.8

Rational points on pencils of conics and quadrics with many degenerate fibres

T. D. Browning^*
, L. Matthiesen
, A. N. Skorobogatov

^*Corresponding author for this work

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

27 Citations (Scopus)

36 Downloads (Pure)

Abstract

For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.

Original language	English
Pages (from-to)	381-402
Number of pages	22
Journal	Annals of Mathematics
Volume	180
Issue number	1
DOIs	https://doi.org/10.4007/annals.2014.180.1.8
Publication status	Published - 1 Jul 2014

Keywords

BINARY QUADRATIC-FORMS
HASSE PRINCIPLE
WEAK APPROXIMATION
PROJECTIVE LINE
DESCENT
SURFACES
FIBRATIONS
VARIETIES
BUNDLES

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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 = "Rational points on pencils of conics and quadrics with many degenerate fibres",

abstract = "For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.",

keywords = "BINARY QUADRATIC-FORMS, HASSE PRINCIPLE, WEAK APPROXIMATION, PROJECTIVE LINE, DESCENT, SURFACES, FIBRATIONS, VARIETIES, BUNDLES",

author = "Browning, \{T. D.\} and L. Matthiesen and Skorobogatov, \{A. N.\}",

year = "2014",

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doi = "10.4007/annals.2014.180.1.8",

language = "English",

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journal = "Annals of Mathematics",

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T1 - Rational points on pencils of conics and quadrics with many degenerate fibres

AU - Browning, T. D.

AU - Matthiesen, L.

AU - Skorobogatov, A. N.

PY - 2014/7/1

Y1 - 2014/7/1

N2 - For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.

AB - For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.

KW - BINARY QUADRATIC-FORMS

KW - HASSE PRINCIPLE

KW - WEAK APPROXIMATION

KW - PROJECTIVE LINE

KW - DESCENT

KW - SURFACES

KW - FIBRATIONS

KW - VARIETIES

KW - BUNDLES

U2 - 10.4007/annals.2014.180.1.8

DO - 10.4007/annals.2014.180.1.8

M3 - Article (Academic Journal)

SN - 0003-486X

VL - 180

SP - 381

EP - 402

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 1

ER -

Rational points on pencils of conics and quadrics with many degenerate fibres

Abstract

Keywords

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DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY

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