The motivic zeta function and its smallest poles

[摘要] Let f be a regular function on a nonsingular complex algebraic variety of dimension d. We prove a formula for the motivic zeta function of f in terms of an embedded resolution. This formula is over the Grothendieck ring itself, and specializes to the formula of Denef and Loeser over a certain localization. We also show that the. space of n-jets satisfying f = 0 can be partitioned into locally closed subsets which are isomorphic to a cartesian product of some variety with an affine space of dimension inverted right perpenticular dn/2 inverted left perpendicular. Finally, we look at the consequences for the poles of the motivic zeta function. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] motivic zeta function;jet spaces