Every function field over K can be regarded as a finite field extension of a rational function field K(x). This is one of the reasons why it is of interest to investigate field extensions F′/F of algebraic function fields. In this chapter we shall study among other things, the relationship between places, divisors, Weil differentials and the genera of F′ and F. Let us first fix some notation to be maintained throughout the entire chapter.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Extensions of Algebraic Function Fields. In: Algebraic Function Fields and Codes. Graduate Texts in Mathematics, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76878-4_3
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DOI: https://doi.org/10.1007/978-3-540-76878-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76877-7
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