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Division algebras and maximal orders for given invariants

Published online by Cambridge University Press:  26 August 2016

Gebhard Böckle  and
Damián Gvirtz
Gebhard Böckle
Affiliation:
Universität Heidelberg, Interdisziplinäres Zentrum für wissenschaftliches Rechnen (IWR), Im Neuenheimer Feld 368, 69120 Heidelberg, Germany email gebhard.boeckle@iwr.uni-heidelberg.de
Damián Gvirtz
Affiliation:
The London School of Geometry and Number Theory, Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom email damian.gvirtz.15@ucl.ac.uk

Abstract

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Brauer classes of a global field can be represented by cyclic algebras. Effective constructions of such algebras and a maximal order therein are given for $\mathbb{F}_{q}(t)$ , excluding cases of wild ramification. As part of the construction, we also obtain a new description of subfields of cyclotomic function fields.

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