Identifying Frobenius elements in Galois groups

Dokchitser, Tim; Dokchitser, Vladimir

doi:10.2140/ant.2013.7.1325

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Identifying Frobenius elements in Galois groups

Tim Dokchitser and Vladimir Dokchitser

Vol. 7 (2013), No. 6, 1325–1352

DOI: 10.2140/ant.2013.7.1325

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/

Vol. 7, No. 6, 2013