Motivic Igusa Zeta Functions
نویسنده
چکیده
Let p be a prime number and let K be a finite extension of Qp. Let R be the valuation ring of K, P the maximal ideal of R, and K̄ = R/P the residue field of K. Let q denote the cardinality of K̄, so K̄ ≃ Fq. For z in K, let ord z denote the valuation of z, and set |z| = q . Let f be a non constant element of K[x1, . . . , xm]. The p-adic Igusa local zeta function Z(s) associated to f (relative to the trivial multiplicative character) is defined as the p-adic integral
منابع مشابه
2 00 0 Zeta Functions and ‘ Kontsevich Invariants ’ on Singular Varieties
Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain motivic integral, living in a completion of the Grotendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi–Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant motivic (Igus...
متن کاملZETA FUNCTIONS AND ` KONTSEVICHINVARIANTS ' ON SINGULAR VARIETIESWillem
Let X be a nonsingular algebraic variety in characteristic zero. To an eeective divisor on X Kontsevich has associated a certain`motivic integral', living in a completion of the Grotendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi{Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant motivic (Igus...
متن کاملQuasi-ordinary Power Series and Their Zeta Functions
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function ZDL(h, T ) of a quasi-ordinary power series h of arbitrary dimension over an algebraically closed field of characteristic zero from its...
متن کاملInvariants ’ on Singular Varieties
Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain ‘motivic integral’, living in a completion of the Grotendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi–Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant motivic (Ig...
متن کاملMotivic Zeta Functions of Infinite Dimensional Lie Algebras
1.1. In the present paper we associate motivic zeta functions to certain classes of infinite dimensional Lie algebra over a field k of characteristic zero. Included in these classes are the important cases of loop algebras, affine Kac-Moody algebras, the Virasoro algebra and Lie algebras of Cartan type. These zeta functions take their values in the Grothendieck ring of algebraic varieties over ...
متن کامل