Riemann surfaces of field extensions
- 1 May 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 65 (3) , 635-650
- https://doi.org/10.1017/s0305004100003431
Abstract
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.Keywords
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