Melle Hernández, Alejandro and Artal Bartolo, Enrique and CassouNoguès, Pierrette and Luengo Velasco, Ignacio (2005) QuasiOrdinary power series and their Zeta functions. Memoirs of the American Mathematical Society , 178 (841). VI85. ISSN 19476221

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Abstract
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasiordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local DenefLoeser motivic zeta function Z(DL)(h,T) of a quasiordinary power series h of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent Z(DL)(h, T) = P(T)/Q(T) such that almost all the candidate poles given by Q(T) are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex R psi(h) of nearby cycles on h(1)(0). In particular we prove in this case the monodromy conjecture made by DenefLoeser for the local motivic zeta function and the local topological zeta function. As a consequence, if h is a quasiordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.
Item Type:  Article 

Uncontrolled Keywords:  Motivic; Topological and Igusa zeta functions; Monodromy; Quasiordinary singularities 
Subjects:  Sciences > Mathematics > Algebraic geometry 
ID Code:  13919 
Deposited On:  18 Nov 2011 08:21 
Last Modified:  06 Feb 2014 09:55 
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