Forms over number fields and weak approximation

C. M. Skinner

doi:10.1023/A:1000129818730

Forms over number fields and weak approximation

C. M. Skinner

Mathematics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

Let K be a number field, and let X ⊆ ℙ^s-1_K be a smooth complete intersection defined over K. In this paper, weak approximation is shown to hold for X provided s exceeds some function of the degree and codimension of X. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method.

Original language	English (US)
Pages (from-to)	11-29
Number of pages	19
Journal	Compositio Mathematica
Volume	106
Issue number	1
DOIs	https://doi.org/10.1023/A:1000129818730
State	Published - 1997

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Forms in many variables
Hardy-Littlewood method
Weak approximation

Access to Document

10.1023/A:1000129818730

Cite this

@article{4c3d5a93e4224bdf8c11730998c83b0f,

title = "Forms over number fields and weak approximation",

abstract = "Let K be a number field, and let X ⊆ ℙs-1K be a smooth complete intersection defined over K. In this paper, weak approximation is shown to hold for X provided s exceeds some function of the degree and codimension of X. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method.",

keywords = "Forms in many variables, Hardy-Littlewood method, Weak approximation",

author = "Skinner, {C. M.}",

note = "Funding Information: Much of this research was completed while the author was a student at the University of Michigan and was supported by an NSF/REU grant. During preparation of this paper he was supported by an NSF Graduate Fellowship and, during a visit to the University of Michigan, by the David and Lucile Packard Foundation.",

year = "1997",

doi = "10.1023/A:1000129818730",

language = "English (US)",

volume = "106",

pages = "11--29",

journal = "Compositio Mathematica",

issn = "0010-437X",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Forms over number fields and weak approximation

AU - Skinner, C. M.

N1 - Funding Information: Much of this research was completed while the author was a student at the University of Michigan and was supported by an NSF/REU grant. During preparation of this paper he was supported by an NSF Graduate Fellowship and, during a visit to the University of Michigan, by the David and Lucile Packard Foundation.

PY - 1997

Y1 - 1997

N2 - Let K be a number field, and let X ⊆ ℙs-1K be a smooth complete intersection defined over K. In this paper, weak approximation is shown to hold for X provided s exceeds some function of the degree and codimension of X. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method.

AB - Let K be a number field, and let X ⊆ ℙs-1K be a smooth complete intersection defined over K. In this paper, weak approximation is shown to hold for X provided s exceeds some function of the degree and codimension of X. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method.

KW - Forms in many variables

KW - Hardy-Littlewood method

KW - Weak approximation

UR - http://www.scopus.com/inward/record.url?scp=0010133282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010133282&partnerID=8YFLogxK

U2 - 10.1023/A:1000129818730

DO - 10.1023/A:1000129818730

M3 - Article

AN - SCOPUS:0010133282

SN - 0010-437X

VL - 106

SP - 11

EP - 29

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 1

ER -

Forms over number fields and weak approximation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this