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On motivic zeta functions and the motivic nearby fiber

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Abstract.

We collect some properties of the motivic zeta functions and the motivic nearby fiber defined by Denef and Loeser. In particular, we calculate the relative dual of the motivic nearby fiber. We give a candidate for a nearby cycle morphism on the level of Grothendieck groups of varieties using the motivic nearby fiber.

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References

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Authors and Affiliations

  1. Universität Essen, FB6, Mathematik, 45117, Essen, Germany

    Franziska Bittner

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  1. Franziska Bittner
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Correspondence to Franziska Bittner.

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Mathematics Subject Classification (1991): 14F42, 32S30

I am indebted to Eduard Looijenga, my thesis advisor. I thank Jan Denef and Wim Veys for their comments and questions. I thank Hélène Esnault and the DFG-Schwerpunkt ‘‘Globale Methoden in der komplexen Geometrie’’ for support while I finished this work.

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Bittner, F. On motivic zeta functions and the motivic nearby fiber. Math. Z. 249, 63–83 (2005). https://doi.org/10.1007/s00209-004-0689-1

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  • DOI: https://doi.org/10.1007/s00209-004-0689-1

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