Solvability of systems of diagonal equations over p-adic local fields

Christopher Skinner

doi:10.1112/plms.12318

Solvability of systems of diagonal equations over p-adic local fields

Christopher Skinner

Mathematics

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

2 Scopus citations

Abstract

We prove that a system of (Formula presented.) diagonal equations of degree (Formula presented.) over a finite extension (Formula presented.) of (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.) (if (Formula presented.)) or (Formula presented.) (if (Formula presented.)). As a consequence, a system of (Formula presented.) homogeneous equations of degree (Formula presented.) over (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.).

Original language	English (US)
Pages (from-to)	207-228
Number of pages	22
Journal	Proceedings of the London Mathematical Society
Volume	122
Issue number	2
DOIs	https://doi.org/10.1112/plms.12318
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

11D72
11D88 (primary)
11E76
11G25 (secondary)

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10.1112/plms.12318

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title = "Solvability of systems of diagonal equations over p-adic local fields",

abstract = "We prove that a system of (Formula presented.) diagonal equations of degree (Formula presented.) over a finite extension (Formula presented.) of (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.) (if (Formula presented.)) or (Formula presented.) (if (Formula presented.)). As a consequence, a system of (Formula presented.) homogeneous equations of degree (Formula presented.) over (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.).",

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N2 - We prove that a system of (Formula presented.) diagonal equations of degree (Formula presented.) over a finite extension (Formula presented.) of (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.) (if (Formula presented.)) or (Formula presented.) (if (Formula presented.)). As a consequence, a system of (Formula presented.) homogeneous equations of degree (Formula presented.) over (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.).

AB - We prove that a system of (Formula presented.) diagonal equations of degree (Formula presented.) over a finite extension (Formula presented.) of (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.) (if (Formula presented.)) or (Formula presented.) (if (Formula presented.)). As a consequence, a system of (Formula presented.) homogeneous equations of degree (Formula presented.) over (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.).

KW - 11D72

KW - 11D88 (primary)

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KW - 11G25 (secondary)

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ER -

Solvability of systems of diagonal equations over p-adic local fields

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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