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Motivic zeta functions in additive monoidal categories

Published online by Cambridge University Press:  08 December 2011

Kenichiro Kimura ,
Shun-ichi Kimura  and
Nobuyoshi Takahashi
Kenichiro Kimura
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571 Japankimurak@math.tsukuba.ac.jp
Shun-ichi Kimura
Affiliation:
Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526 Japankimura@math.sci.hiroshima-u.ac.jp
Nobuyoshi Takahashi
Affiliation:
Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526 Japantakahasi@math.sci.hiroshima-u.ac.jp
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Abstract

Let C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C. We study the problem of rationality of the motivic zeta function ζx(t) of X. Since the coefficient ring is not a field, there are several variants of rationality — uniform, global, determinantal and pointwise rationality. We show that ζx(t) is determinantally rational, and we give an example of C and X for which the motivic zeta function is not uniformly rational.

Keywords

Motivic zeta functionmonoidal categoryrationality
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 3 , June 2012 , pp. 459 - 473
Copyright
Copyright © ISOPP 2011

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