Elementary Abelianp-extensions of algebraic function fields |
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Authors: | Arnaldo Garcia Henning Stichtenoth |
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Institution: | 1. Pura e Aplicada, Instituto de Matematica, Estrada Dona Castorina 110, 22.460, Rio de Janeiro, Brazil 2. Fachbereich 6-Mathematik, Universit?t GHS Essen, D-4300, Essen 1, Fed. Rep. Germany
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Abstract: | LetK be a field of characteristicp>0 andF/K be an algebraic function field. We obtain several results on Galois extensionsE/F with an elementary Abelian Galois group of orderp n. - E can be generated overF by some elementy whose minimal polynomial has the specific formT pn?T?z.
- A formula for the genus ofE is given.
- IfK is finite, then the genus ofE grows much faster than the number of rational points (as E∶F] → ∞).
- We present a new example of a function fieldE/K whose gap numbers are nonclassical.
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