Diagonal equations over unramified extensions of Qp

David B. Leep; Luis Sordo Vieira

doi:10.1112/blms.12163

Diagonal equations over unramified extensions of Q_p

David B. Leep, Luis Sordo Vieira

Mathematics

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

6 Scopus citations

Abstract

If K is an unramified extension of the p -adic field Q_p where p ≥ 3, then we prove that any diagonal homogeneous form defined over K of degree d has a nontrivial zero in K provided that the number of variables is greater than d².

Original language	English
Pages (from-to)	619-634
Number of pages	16
Journal	Bulletin of the London Mathematical Society
Volume	50
Issue number	4
DOIs	https://doi.org/10.1112/blms.12163
State	Published - Aug 2018

Bibliographical note

Publisher Copyright:
© 2018 London Mathematical Society

Keywords

11D72 (secondary)
11D88
11E76 (primary)

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/blms.12163

Cite this

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title = "Diagonal equations over unramified extensions of Qp ",

abstract = "If K is an unramified extension of the p -adic field Qp where p ≥ 3, then we prove that any diagonal homogeneous form defined over K of degree d has a nontrivial zero in K provided that the number of variables is greater than d2.",

keywords = "11D72 (secondary), 11D88, 11E76 (primary)",

author = "Leep, {David B.} and {Sordo Vieira}, Luis",

note = "Publisher Copyright: {\textcopyright} 2018 London Mathematical Society",

year = "2018",

month = aug,

doi = "10.1112/blms.12163",

language = "English",

volume = "50",

pages = "619--634",

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AU - Sordo Vieira, Luis

PY - 2018/8

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N2 - If K is an unramified extension of the p -adic field Qp where p ≥ 3, then we prove that any diagonal homogeneous form defined over K of degree d has a nontrivial zero in K provided that the number of variables is greater than d2.

AB - If K is an unramified extension of the p -adic field Qp where p ≥ 3, then we prove that any diagonal homogeneous form defined over K of degree d has a nontrivial zero in K provided that the number of variables is greater than d2.

KW - 11D72 (secondary)

KW - 11D88

KW - 11E76 (primary)

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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