Motivic Igusa zeta functions

Details Motivic Igusa zeta functions Motivic Igusa zeta functions

1998-03-11

arxiv.org/abs/math/9803040v1

J. Algebraic Geom. 7 (1998), no. 3, 505--537

Mathematics

Algebraic Geometry

Revised September 1997, to appear in Journal of Algebraic Geometry, 34 pages

Scientific paper

We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the topological zeta functions we introduced several years ago. We study their basic properties, such as functional equations, and their relation with motivic nearby cycles. In particular the Hodge spectrum of a singular point of a function may be recovered from the Hodge realization of these zeta functions.

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