Weak approximation for cubic hypersurfaces of large dimension

Michael P Swarbrick Jones

doi:10.2140/ant.2013.7.1353

Weak approximation for cubic hypersurfaces of large dimension

Michael P Swarbrick Jones

School of Mathematics

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

2 Citations (Scopus)

Abstract

We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.

Original language	English
Pages (from-to)	1353-1363
Number of pages	11
Journal	Algebra and Number Theory
Volume	7
Issue number	6
DOIs	https://doi.org/10.2140/ant.2013.7.1353
Publication status	Published - 2013

Keywords

cubic hypersurfaces
weak approximation
local-global principles
fibration method
circle method
many variables
NUMBER-FIELDS
SURFACES

Access to Document

10.2140/ant.2013.7.1353

Handle.net

Persistent link

Cite this

@article{1336809bb1f5461aa116e4602663a6b3,

title = "Weak approximation for cubic hypersurfaces of large dimension",

abstract = "We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.",

keywords = "cubic hypersurfaces, weak approximation, local-global principles, fibration method, circle method, many variables, NUMBER-FIELDS, SURFACES",

author = "{Swarbrick Jones}, {Michael P}",

year = "2013",

doi = "10.2140/ant.2013.7.1353",

language = "English",

volume = "7",

pages = "1353--1363",

journal = "Algebra and Number Theory",

issn = "1937-0652",

publisher = "Mathematical Sciences Publishers",

number = "6",

}

TY - JOUR

T1 - Weak approximation for cubic hypersurfaces of large dimension

AU - Swarbrick Jones, Michael P

PY - 2013

Y1 - 2013

N2 - We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.

AB - We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.

KW - cubic hypersurfaces

KW - weak approximation

KW - local-global principles

KW - fibration method

KW - circle method

KW - many variables

KW - NUMBER-FIELDS

KW - SURFACES

U2 - 10.2140/ant.2013.7.1353

DO - 10.2140/ant.2013.7.1353

M3 - Article (Academic Journal)

SN - 1937-0652

VL - 7

SP - 1353

EP - 1363

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 6

ER -

Weak approximation for cubic hypersurfaces of large dimension

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this