Vol. 7, No. 6, 2013

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Identifying Frobenius elements in Galois groups

Tim Dokchitser and Vladimir Dokchitser

Vol. 7 (2013), No. 6, 1325–1352
Abstract

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.

Keywords
Frobenius elements, Artin representations, Galois groups
Mathematical Subject Classification 2010
Primary: 11R32
Secondary: 11R42, 12F10
Milestones
Received: 4 August 2011
Revised: 9 May 2012
Accepted: 7 June 2012
Published: 19 September 2013
Authors
Tim Dokchitser
Department of Mathematics
Bristol University
University Walk
Bristol
BS8 1TW
United Kingdom
http://www.maths.bris.ac.uk/~matyd/
Vladimir Dokchitser
Emmanuel College
University of Cambridge
Cambridge
CB2 3AP
United Kingdom
http://www.dpmms.cam.ac.uk/~vd209/