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On the Computation of Integral Closures of Cyclic Extensions of Function Fields

Published online by Cambridge University Press:  01 February 2010

Robert Fraatz
Robert Fraatz
Affiliation:
Technische Universität Berlin, Fakultät II, Institut für Mathematik MA 8–1, Straße des 17. Juni 136, 10623 Berlin, Germany, fraatz@math.tu-berlin.de, http://www.math.tu-berlin.de/~fraatz

Abstract

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Let S be a non-empty proper subset of the set of places of a global function field F and E a cyclic Kummer or Artin–Schreier–Witt extension of F. We present a method of efficiently computing the ring of elements of E which are integral at all places of S. As an important tool, we include an algorithmic version of the strong approximation theorem. We conclude with several examples.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 10 , 2007 , pp. 141 - 160
Copyright
Copyright © London Mathematical Society 2007

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