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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2006 Volume 252, Pages 71–82 (Mi tm63)

This article is cited in 5 papers

Integration over Spaces of Nonparametrized Arcs and Motivic Versions of the Monodromy Zeta Function

S. M. Gusein-Zadea, I. Luengob, A. Melle-Hernándezb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Universidad Complutense de Madrid

Abstract: Notions of integration of motivic type over the space of arcs factorized by the natural $\mathbb C^*$-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on $\mathbb C^d$ are given that correspond to these notions. Another key ingredient in the construction of these motivic versions of the zeta function is the use of the so-called power structure over the Grothendieck ring of varieties introduced by the authors.

UDC: 515.165

Received in May 2005


 English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 252, 63–73

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