Forms in many variables and differing degrees

Tim Browning; Roger Heath-Brown

doi:10.4171/JEMS/668

Forms in many variables and differing degrees

Tim Browning, Roger Heath-Brown

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

27 Citations (Scopus)

291 Downloads (Pure)

Abstract

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X P^m, provided only that its dimension is large enough in terms of its degree.

Original language	English
Pages (from-to)	357-394
Number of pages	38
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/668
Publication status	Published - 26 Jan 2017

Keywords

Complete intersections
Forms in many variables
Hardy-Littlewood circle method
Hasse principle
Rational points Manin conjecture
Weak approximation

Access to Document

10.4171/JEMS/668

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via EMS at http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=19&iss=2&rank=2 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 402 KB

Handle.net

Persistent link

Cite this

@article{94a5fd04157449e4b3d3a5d738e4ac50,

title = "Forms in many variables and differing degrees",

abstract = "We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.",

keywords = "Complete intersections, Forms in many variables, Hardy-Littlewood circle method, Hasse principle, Rational points Manin conjecture, Weak approximation",

author = "Tim Browning and Roger Heath-Brown",

year = "2017",

month = jan,

day = "26",

doi = "10.4171/JEMS/668",

language = "English",

volume = "19",

pages = "357--394",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Forms in many variables and differing degrees

AU - Browning, Tim

AU - Heath-Brown, Roger

PY - 2017/1/26

Y1 - 2017/1/26

N2 - We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.

AB - We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.

KW - Complete intersections

KW - Forms in many variables

KW - Hardy-Littlewood circle method

KW - Hasse principle

KW - Rational points Manin conjecture

KW - Weak approximation

UR - http://www.scopus.com/inward/record.url?scp=85011004552&partnerID=8YFLogxK

U2 - 10.4171/JEMS/668

DO - 10.4171/JEMS/668

M3 - Article (Academic Journal)

SN - 1435-9855

VL - 19

SP - 357

EP - 394

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 2

ER -

Forms in many variables and differing degrees

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Embargoed Document

Fingerprint

Cite this