We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.
Nous considérons les fonctions zêta à valeurs dans l’anneau de Grothendieck des motifs de Chow. L’étude de la -structure de cet anneau, nous permet d’obtenir une équation fonctionnelle pour la fonction zêta des variétés abéliennes. En outre nous montrons que l’existence d’une telle équation fonctionnelle est une propriété stable par produit.
Keywords: zeta functions, Chow motives, functional equation
Mot clés : fonctions zêta, motifs de Chow, équation fonctionnelle
Heinloth, Franziska 1
@article{AIF_2007__57_6_1927_0, author = {Heinloth, Franziska}, title = {A note on functional equations for zeta functions with values in {Chow} motives}, journal = {Annales de l'Institut Fourier}, pages = {1927--1945}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {6}, year = {2007}, doi = {10.5802/aif.2318}, mrnumber = {2377891}, zbl = {1154.14018}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2318/} }
TY - JOUR AU - Heinloth, Franziska TI - A note on functional equations for zeta functions with values in Chow motives JO - Annales de l'Institut Fourier PY - 2007 SP - 1927 EP - 1945 VL - 57 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2318/ DO - 10.5802/aif.2318 LA - en ID - AIF_2007__57_6_1927_0 ER -
%0 Journal Article %A Heinloth, Franziska %T A note on functional equations for zeta functions with values in Chow motives %J Annales de l'Institut Fourier %D 2007 %P 1927-1945 %V 57 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2318/ %R 10.5802/aif.2318 %G en %F AIF_2007__57_6_1927_0
Heinloth, Franziska. A note on functional equations for zeta functions with values in Chow motives. Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 1927-1945. doi : 10.5802/aif.2318. https://aif.centre-mersenne.org/articles/10.5802/aif.2318/
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