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arXiv · 0710.5911

The motivic zeta function and its smallest poles

Dirk Segers·Lise Van Proeyen·Willem Veys
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Abstract

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 the round up of dn/2. Finally, we look at the consequences for the poles of the motivic zeta function.

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Dirk Segers, Lise Van Proeyen, Willem Veys. 2012-09-17. The motivic zeta function and its smallest poles. https://doi.org/10.1016/j.jalgebra.2007.05.012

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