A short proof for the relation between Weil indices and factors

Dani Szpruch

doi:10.1080/00927872.2017.1399407

A short proof for the relation between Weil indices and factors

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Abstract

Let F be a finite extension of ℚ_p and let ψ be a non-trivial character of F. For a∈F* let γ(a,ψ) be the normalized Weil index splitting the Hilbert symbol. In this short note we give a simple proof for the relation (Formula presented.) where η_a is the quadratic character of F* whose kernel is N(F√a) and where &(⋅,⋅,⋅) is the epsilon factor appearing in Tate’s thesis.

Original language	English
Pages (from-to)	2846-2851
Number of pages	6
Journal	Communications in Algebra
Volume	46
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2017.1399407
State	Published - 3 Jul 2018
Externally published	Yes

Keywords

Epsilon factor
Hilbert symbol
Weil index
local factors

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1080/00927872.2017.1399407

Cite this

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AB - Let F be a finite extension of ℚp and let ψ be a non-trivial character of F. For a∈F* let γ(a,ψ) be the normalized Weil index splitting the Hilbert symbol. In this short note we give a simple proof for the relation (Formula presented.) where ηa is the quadratic character of F* whose kernel is N(F√a) and where &(⋅,⋅,⋅) is the epsilon factor appearing in Tate’s thesis.

KW - Epsilon factor

KW - Hilbert symbol

KW - Weil index

KW - local factors

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DO - 10.1080/00927872.2017.1399407

M3 - مقالة

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SP - 2846

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

A short proof for the relation between Weil indices and factors

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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