scholarly journals Codes and the Cartier operator

2014 ◽  
Vol 142 (6) ◽  
pp. 1983-1996 ◽  
Author(s):  
Alain Couvreur
Keyword(s):  
Cartier Operator

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).

The trace of the cartier operator and character sums

1990 ◽  
Vol 18 (11) ◽  
pp. 3689-3703
Author(s):  
Amílcar Pacheco
Keyword(s):  
Character Sums ◽  
Cartier Operator

On the Jacobson-Cartier Operator

1978 ◽  
Vol s2-18 (2) ◽  
pp. 202-208
Author(s):  
S. K. Gupta
Keyword(s):  
Cartier Operator

scholarly journals A bound on the genus of a curve with Cartier operator of small rank

2018 ◽  
Vol 68 (3) ◽  
pp. 569-577
Author(s):  
Zijian Zhou
Keyword(s):  
Small Rank ◽  
Cartier Operator

Abstract Ekedahl showed that the genus of a curve in characteristic $$p>0$$ p > 0 with zero Cartier operator is bounded by $$p(p-1)/2$$ p ( p - 1 ) / 2 . We show the bound $$p+p(p-1)/2$$ p + p ( p - 1 ) / 2 in case the rank of the Cartier operator is 1, improving a result of Re.

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