Motives for perfect PAC fields with pro-cyclic Galois group

Details Motives for perfect PAC fields with pro-cyclic Galois group Motives for perfect PAC fields with pro-cyclic Galois group

2007-04-17

arxiv.org/abs/0704.2206v2

J. Symbolic Logic, 73 (2008), pp. 1036-1050

Mathematics

Logic

15 pages, to appear in JSL; minor corrections and one proof replaced by a sketch of proof and a reference

Scientific paper

Denef and Loeser defined 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.

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