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Mathematics of Computation

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The infrastructure of a global field of arbitrary unit rank


Author: Felix Fontein
Journal: Math. Comp. 80 (2011), 2325-2357
MSC (2010): Primary 11Y40; Secondary 14H05, 11R27, 11R65
DOI: https://doi.org/10.1090/S0025-5718-2011-02490-7
Published electronically: April 26, 2011
MathSciNet review: 2813364
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Abstract: In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and $ f$-representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish that effective implementation of the presented methods is indeed possible, and we show how Shanks' baby-step giant-step method can be generalized to this situation.


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Additional Information

Felix Fontein
Affiliation: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
Address at time of publication: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
Email: felix.fontein@math.uzh.ch

DOI: https://doi.org/10.1090/S0025-5718-2011-02490-7
Keywords: Infrastructures, giant steps, number fields, function fields, Riemann-Roch spaces, fundamental units
Received by editor(s): January 26, 2009
Received by editor(s) in revised form: October 7, 2010
Published electronically: April 26, 2011
Additional Notes: This work was supported in part by the Swiss National Science Foundation under grant no. 107887.
Article copyright: © Copyright 2011 Felix Fontein

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