Ramified Coverings and Galois Theory

Askold Khovanskii
Additional contact information
Askold Khovanskii: University of Toronto, Dept. Mathematics

Chapter Chapter 3 in Galois Theory, Coverings, and Riemann Surfaces, 2013, pp 65-77 from Springer

Abstract: Abstract The third chapter contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface. For such surfaces, the geometry of ramified coverings and Galois theory are not only analogous but in fact very closely related to each other. This relationship is useful in both directions. On the one hand, Galois theory and Riemann’s existence theorem allow one to describe the field of functions on a ramified covering over a Riemann surface as a finite algebraic extension of the field of meromorphic functions on the Riemann surface. On the other hand, the geometry of ramified coverings together with Riemann’s existence theorem allows one to give a transparent description of algebraic extensions of the field of meromorphic functions over a Riemann surface.

Keywords: Riemann Surface; Meromorphic Function; Fundamental Group; Galois Group; Multivalued Function (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-38841-5_3

Ordering information: This item can be ordered from
http://www.springer.com/9783642388415

DOI: 10.1007/978-3-642-38841-5_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().