Title: Relative motives and the theory of pseudo-finite fields
Authors: Nicaise, Johannes # ×
Issue Date: 2007
Publisher: Oxford University Press
Series Title: International Mathematics Research Papers vol:2007 issue:1 pages:1-70
Abstract: We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow motives over S, and we show how to associate a motive to any S-variety. We give a geometric proof of relative quantifier elimination for pseudo-finite fields, and we construct a morphism from the Grothendieck ring of the theory of pseudo-finite fields over S, to the tensor product of Q with the Grothendieck ring of constructible effective Chow motives. This morphism yields a motivic realization of parameterized arithmetic integrals. Finally, we define relative arc and jet spaces, and the three relative motivic Poincare series.
ISSN: 1687-3017
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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