(1) Laboratoire de Mathématiques Nicolas Oresme, C.N.R.S.-UMR 6139, Université de Caen, 14 032 Caen cedex, France;(2) Unité de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46, allée dItalie, 69 363 Lyon cedex 7, France
Abstract:
We prove, as an analogy of a conjecture of Artin, that if is a finite flat morphism between two singular reduced absolutely irreducible projectivealgebraic curves defined over a finite field, then the numerator of the zeta functionof X divides that of Yin . Then, we give some interpretations of this result in terms of semi-abelian varieties.Received: 23 July 2001
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Italie, 69 363 Lyon cedex 7, France
is a finite flat morphism between two singular reduced absolutely irreducible projectivealgebraic curves defined over a finite field, then the numerator of the zeta functionof X divides that of Yin ![$ mathbb{Z}[T] $](/content/68jg0568ejbyjlwk/13_2003_Article_4606_TeX2GIFIEq2.gif)
. Then, we give some interpretations of this result in terms of semi-abelian varieties.Received: 23 July 2001