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Motives for perfect PAC fields with pro-cyclic Galois group

Published online by Cambridge University Press:  12 March 2014

Immanuel Halupczok
Immanuel Halupczok*
Affiliation:
Ecole Normale Supérieure, DMA, 45, Rue D'ulm, 75230 Paris Cedex 05, France, E-mail: [email protected]
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Abstract

Denef and Loeser denned a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group.

In addition, we define some maps between different Grothendieck rings of definable sets which provide additional information, not contained in the associated motive. In particular we infer that the map of Denef-Loeser is not injective.

Keywords

Pseudo-finite fieldspseudo algebraically closed fieldsmotives
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 1036 - 1050
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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