Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem

  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 210)


Having developed all the basic material we will need about function fields we now proceed to discuss extensions of function fields. This material can be presented in a geometric fashion. Function fields correspond to algebraic curves and finite extensions of function fields correspond to ramified covers of curves. In this chapter, however, we will continue to use a more arithmetic point of view which emphasizes the analogy of function fields with algebraic number fields.


Function Field Constant Field Finite Extension Weierstrass Point Discrete Valuation Ring 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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