Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem
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.
KeywordsFunction Field Constant Field Finite Extension Weierstrass Point Discrete Valuation Ring
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