Divisibility of zeta functions of curves in a covering

被引：10

作者：

Aubry, Y ^{[1
]}

Perret, M

机构：

[1] Univ Caen, CNRS, UMR 6139, Lab Math Nicolas Oresme, F-14032 Caen, France

[2] Ecole Normale Super Lyon, Unite Math Pures & Appl, F-69636 Lyon 7, France

[3] CNRS, Inst Math Luminy, Marseille, France

来源：

ARCHIV DER MATHEMATIK | 2004年 / 82卷 / 03期

关键词：

D O I：

10.1007/s00013-003-4606-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove, as an analogy of a conjecture of Artin, that if Y --> X is a finite flat morphism between two singular reduced absolutely irreducible projective algebraic curves defined over a finite field, then the numerator of the zeta function of X divides that of Y in Z[T]. Then, we give some interpretations of this result in terms of semi-abelian varieties.

引用

页码：205 / 213

页数：9

共 8 条

[1] Coverings of singular curves over finite fields [J].

Aubry, Y ;

Perret, M .

MANUSCRIPTA MATHEMATICA, 1995, 88 (04) :467-478

[2]

Aubry Y, 1996, ARITHMETIC, GEOMETRY AND CODING THEORY, P1

[3] Weil bounds for singular curves [J].

Bach, E .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1996, 7 (04) :289-298

[4]

DELIGNE P, 1980, PUBL MATH-PARIS, V52, P137, DOI [10.1007/BF02684780. MR0601520, DOI 10.1007/BF02684780.MR0601520]

[5]

Deligne P., 1974, PUBL MATH IHES, V44, P5

[6] THE NUMBER OF POINTS ON A SINGULAR CURVE OVER A FINITE-FIELD [J].

LEEP, DB ;

YEOMANS, CC .

ARCHIV DER MATHEMATIK, 1994, 63 (05) :420-426

[7]

Tate J., 1966, INVENT MATH, V2, P134, DOI DOI 10.1007/BF01404549

[8]

[No title captured]

← 1 →