Abstract
As part of algebraic number theory, Galois theory deals with greatest common divisors (gcd’s, also called ideals) and their conjugates (Stark 1992). One studies how the automorphisms of a field K change a gcd, or a number, to a conjugate. The set of ‘prime gcd’s’ of K may be viewed as a topological space, as is now classical in algebraic geometry. Without going into this, we mention it to motivate the fact that Galois theory may have a meaning in a topological context. And it does indeed, in the context of coverings.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beukers, F. (1990) Differential Galois theory; this volume.
Cohen, H. (1990) Elliptic curves; this volume.
Dèbes, P., Fried, M. (1990) Non rigid situations in constructive Galois theory; preprint 1990.
Douady, R., Douady, A. (1979) Algèbre et théories galoisiennes; Cedic Fernand Nathan (1979).
Reyssat, E. (1989) Quelques aspects des surfaces de Riemann; Birkhäuser (1989).
Serre, J.-P. (1988) Groupes de Galois sur ℚ; Séminaire Bourbaki nr. 689, Astérisque 161-162 (1988) 73–85.
Stark, H. (1992) Galois theory, algebraic number theory and zeta functions; this volume.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Reyssat, E. (1992). Galois Theory for Coverings and Riemann Surfaces. In: Waldschmidt, M., Moussa, P., Luck, JM., Itzykson, C. (eds) From Number Theory to Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02838-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-02838-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08097-5
Online ISBN: 978-3-662-02838-4
eBook Packages: Springer Book Archive