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Residue Free Differentials and the Cartier Operator for Algebraic Function Fields of one Variable

Published online by Cambridge University Press:  20 November 2018

Tetsuo Kodama
Tetsuo Kodama*
Affiliation:
Kyushu University, Fukuoka, Japan
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Let K be a field of characteristic p > 0 and let A be a separably generated algebraic function field of one variable with K as its exact constant field. Throughout this paper we shall use the following notations to classify differentials of A/K:

D(A) : the K-module of all differentials,

G(A) : the K-module of all differentials of the first kind,

R(A) : the K-module of all residue free differentials in the sense of Chevalley [2, p. 48],

E*(A) : the K-module of all pseudo-exact differentials in the sense of Lamprecht [7, p. 363], (compare the definition with our Lemma 8).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 905 - 914
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Arima, S., Locally pseudo-exact differential form in algebraic function fields of non-zero characteristic. Arch. Math. 17 (1966), 409–414.Google Scholar
2. Chevalley, C., Introduction to the theory of algebraic functions of one variable (Amer. Math. Soc, New York, 1951).Google Scholar
3. Deuring, M., Lectures on the theory of algebraic functions of one variable (Tata Institute, Bombay, 1959).Google Scholar
4. Eichler, M., Einführung in die Theorie der algebraischen Zahlen und Funktionen (Birkhäuser Verlag, Basel 1963).Google Scholar
5. Kodama, T., Residuefreie Differentiate und der Cartier-Operator algebraischer Funktionenkörper, Arch. Math. 22 (1971), 271–274.Google Scholar
6. Kunz, E., Einige Anwendungen des Cartier-Operator, Arch. Math. 13 (1962) 349–356.Google Scholar
7. Lamprecht, E., Klassifikation von Differentialen in Körper von Primzahlcharakteristik I, Math. Nachr. 19 (1958), 353–374.Google Scholar
8. Rosenlicht, M., Differentials of the second kind for algebraic function fields of one variable. Ann. of Math. II. Ser. 57 (1953), 514–523.Google Scholar