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

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

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

Bibliographical note

Funding Information:
The author is partially supported by a Simons Foundation Collaboration Grant 426446.

Publisher Copyright:
© 2017 Taylor & Francis.

Keywords

Epsilon factor
Hilbert symbol
Weil index
local factors

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10.1080/00927872.2017.1399407

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A short proof for the relation between Weil indices and factors

Abstract

Bibliographical note

Keywords

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