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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

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