The monodromy conjecture for zeta functions associated to ideals in dimension two
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Publication:1958976
DOI10.5802/AIF.2557zbMATH Open1211.14021arXiv0910.2179OpenAlexW2962952388WikidataQ122903119 ScholiaQ122903119MaRDI QIDQ1958976
Author name not available (Why is that?)
Publication date: 30 September 2010
Published in: (Search for Journal in Brave)
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 a polynomial in two variables. In this article we consider 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.
Full work available at URL: https://arxiv.org/abs/0910.2179
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