Formal deformations of algebraic spaces and generalizations of the motivic Igusa zeta function

Author:

Andrew R. Stout

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

Contemp. Math., Vol. 724, pages 137 - 147, (2019)

date:

2023-09-25 16:00:00

Abstract

We generalize the notion of the auto-Igusa zeta function to formal deformations of algebraic spaces. By incorporating data from all algebraic transformations of local coordinates, this function can be viewed as a generalization of the traditional motivic Igusa zeta function. Furthermore, we introduce a new series, which we term the canonical auto-Igusa zeta function, whose coefficients are given by the quotient stacks formed from the coefficients of the auto-Igusa zeta function modulo change of coordinates. We indicate the current state of the literature on these generalized Igusa-zeta functions and offer directions for future research.

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