Zeta functions and Alexander modules
| dc.creator | Nicaise, Johannes | |
| dc.date | 2004-04-10 | |
| dc.date.accessioned | 2026-07-07T05:07:21Z | |
| dc.date.available | 2026-07-07T05:07:21Z | |
| dc.description | 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. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404212 | |
| dc.identifier | http://arxiv.org/abs/math/0404212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70825 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Zeta functions and Alexander modules | |
| dc.type | text |