Zeta functions and Alexander modules

Details Zeta functions and Alexander modules Zeta functions and Alexander modules

2004-04-10

arxiv.org/abs/math/0404212v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We introduce the etale framework to study Igusa zeta functions in several variables, generalizing the machinery of vanishing cycles in the univariate case. We define the etale Alexander modules, associated to a morphism of varieties F from X to affine r-space, a geometric point of X, and an object in the derived category of constructible l-adic sheaves on the inverse image of the r-torus under F. The Alexander modules are sheaves of modules on the scheme of continuous characters of the tame fundamental group of the r-torus. We formulate Loeser's Monodromy and Holomorphy Conjectures for multivariate p-adic zeta functions, and prove them in the case where dim(X)=2, generalizing results from the univariate case. Furthermore, we prove a comparison theorem with the transcendent case, we study a formula of Denef's for the zeta function in terms of a simultaneous embedded resolution, and we generalize a result concerning the degree of the zeta function to our setting.

Affiliated with

Also associated with

No associations

Rating

Zeta functions and Alexander modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Zeta functions and Alexander modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Zeta functions and Alexander modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-494397