scholarly journals The genus field of an algebraic function field

1992 ◽  
Vol 40 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Rosario Clement
Keyword(s):  
Function Field ◽  
Algebraic Function ◽  
Algebraic Function Field ◽  
Genus Field

scholarly journals On holomorphic differentials of some algebraic function field of one variable over C

1991 ◽  
Vol 43 (3) ◽  
pp. 399-405 ◽  
Author(s):  
Ja Kyung Koo
Keyword(s):  
Function Field ◽  
Algebraic Function ◽  
Algebraic Function Field ◽  
Complex Dimension ◽  
Dimension One

We give holomorphic differentials of some algebraic function field K of complex dimension one which is a generalisation of a hyperelliptic field.

scholarly journals Linear Dynamical Systems of Higher Genus

1994 ◽  
Vol 1 (5) ◽  
pp. 505-521
Author(s):  
V. Lomadze
Keyword(s):  
Dynamical Systems ◽  
Linear Systems ◽  
Rational Function ◽  
Function Field ◽  
Algebraic Function ◽  
Linear Dynamical Systems ◽  
Algebraic Function Field ◽  
Rational Function Field ◽  
Higher Genus

Abstract A class of linear systems which after ordinary linear systems are in a certain sense the simplest ones, is associated with every algebraic function field. From the standpoint developed in the paper ordinary linear systems are associated with the rational function field.

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

1972 ◽  
Vol 24 (5) ◽  
pp. 905-914
Author(s):  
Tetsuo Kodama
Keyword(s):  
Function Field ◽  
Function Fields ◽  
Algebraic Function ◽  
Exact Constant ◽  
Constant Field ◽  
Algebraic Function Field ◽  
Algebraic Function Fields ◽  
Cartier Operator

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).

On Rationality of Algebraic Function Fields

1969 ◽  
Vol 12 (3) ◽  
pp. 339-341 ◽  
Author(s):  
Nobuo Nobusawa
Keyword(s):  
Rational Function ◽  
Number Field ◽  
Algebraic Number ◽  
Function Field ◽  
Algebraic Function ◽  
Algebraic Number Field ◽  
Constant Field ◽  
Algebraic Function Field ◽  
Algebraic Function Fields ◽  
Transcendental Extension

Let A be an algebraic function field with a constant field k which is an algebraic number field. For each prime p of k, we consider a local completion kp and set Ap = Ak ꕕ kp. Then we have the question:Is it true that A/k is a rational function field (i.e., A is a purely transcendental extension of k) if Ap/kp is so for every p ? In this note we shall discuss the question in a slightly different and hence easier case.

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