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Coverings of Singular Curves over Finite Fields Yves Aubry1
 

Summary: Coverings of Singular Curves over Finite Fields
Yves Aubry1
, Marc Perret2
1
D´epartement de Math´ematiques, Universit´e de Caen
Esplanade de la Paix - 14 032 Caen Cedex - France.
2
Unit´e de Math´ematiques, ´Ecole Normale Sup´erieure de Lyon
46, all´ee d'Italie - 69 363 Lyon Cedex 7 - France.
We prove that if f : Y - X is a finite flat morphism between
two reduced absolutely irreducible algebraic projective curves
defined over the finite field Fq, then
| Y (Fq) - X(Fq) | 2(Y - X)

q,
where C is the arithmetic genus of a curve C. As application,
we give some character sum estimation on singular curves.
Y. Aubry, M. Perret
In this paper, the word curve stands for a reduced abso-
lutely irreducible algebraic projective curve defined over the

  

Source: Aubry, Yves - Institut de Mathématiques de Toulon, Université du Sud Toulon -Var

 

Collections: Mathematics