The monodromy conjecture for zeta functions associated to ideals in dimension two

Lise Van Proeyen[1]; Willem Veys[1]

  • [1] K.U. Leuven Departement Wiskunde Celestijnenlaan 200B 3001 Leuven (Belgium)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 4, page 1347-1362
  • ISSN: 0373-0956

Abstract

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The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an ideal. Afterwards we prove a generalized monodromy conjecture for arbitrary ideals in two variables.

How to cite

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Van Proeyen, Lise, and Veys, Willem. "The monodromy conjecture for zeta functions associated to ideals in dimension two." Annales de l’institut Fourier 60.4 (2010): 1347-1362. <http://eudml.org/doc/116306>.

@article{VanProeyen2010,
abstract = {The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an ideal. Afterwards we prove a generalized monodromy conjecture for arbitrary ideals in two variables.},
affiliation = {K.U. Leuven Departement Wiskunde Celestijnenlaan 200B 3001 Leuven (Belgium); K.U. Leuven Departement Wiskunde Celestijnenlaan 200B 3001 Leuven (Belgium)},
author = {Van Proeyen, Lise, Veys, Willem},
journal = {Annales de l’institut Fourier},
keywords = {Zeta functions for ideals; Verdier monodromy; monodromy conjecture; topological zeta functions for ideals},
language = {eng},
number = {4},
pages = {1347-1362},
publisher = {Association des Annales de l’institut Fourier},
title = {The monodromy conjecture for zeta functions associated to ideals in dimension two},
url = {http://eudml.org/doc/116306},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Van Proeyen, Lise
AU - Veys, Willem
TI - The monodromy conjecture for zeta functions associated to ideals in dimension two
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1347
EP - 1362
AB - The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an ideal. Afterwards we prove a generalized monodromy conjecture for arbitrary ideals in two variables.
LA - eng
KW - Zeta functions for ideals; Verdier monodromy; monodromy conjecture; topological zeta functions for ideals
UR - http://eudml.org/doc/116306
ER -

References

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