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Riemann surfaces of field extensions

Published online by Cambridge University Press:  24 October 2008

J. T. Knight
J. T. Knight
Affiliation:
United College, Chinese University of Hong Kong†
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Extract

Since Riemann's dissertation of 1851, Riemann surfaces have for the most part been considered as suitable domains of definition for analytic functions. Here, however, we view them as topological spaces associated with certain kinds of field extension, and consider how their topological properties are connected with algebraic properties of these field extensions. A specialization of these results gives us arithmetic properties of fields of algebraic functions of one real variable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 635 - 650
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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