Algebra & Number Theory

Identifying Frobenius elements in Galois groups

Tim Dokchitser and Vladimir Dokchitser

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We present a method to determine Frobenius elements in arbitrary Galois extensions of global fields, which may be seen as a generalisation of Euler’s criterion. It is a part of the general question how to compare splitting fields and identify conjugacy classes in Galois groups, which we will discuss as well.

Article information

Algebra Number Theory, Volume 7, Number 6 (2013), 1325-1352.

Received: 4 August 2011
Revised: 9 May 2012
Accepted: 7 June 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R32: Galois theory
Secondary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 12F10: Separable extensions, Galois theory

Frobenius elements Artin representations Galois groups


Dokchitser, Tim; Dokchitser, Vladimir. Identifying Frobenius elements in Galois groups. Algebra Number Theory 7 (2013), no. 6, 1325--1352. doi:10.2140/ant.2013.7.1325.

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