Motivic Igusa zeta functions
Abstract
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 padic 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 1998
 DOI:
 10.48550/arXiv.math/9803040
 arXiv:
 arXiv:math/9803040
 Bibcode:
 1998math......3040D
 Keywords:

 Mathematics  Algebraic Geometry;
 14A15;
 14A20;
 14B05;
 32S45;
 32S05;
 32S30;
 32S35
 EPrint:
 Revised September 1997, to appear in Journal of Algebraic Geometry, 34 pages