Germs of arcs on singular algebraic varieties and motivic integration

Niveau: Supérieur
Germs of arcs on singular algebraic varieties and motivic integration Jan Denef 1 , Franc¸ois Loeser 2;3 1 University of Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium () 2 Centre de Mathe matiques, Ecole Polytechnique, F-91128 Palaiseau (URA 169 du CNRS) () 3 Institut de Mathe matiques, Universite P. et M. Curie, Case 82, 4 place Jussieu, F-75252 Paris Cedex 05 (UMR 9994 du CNRS) Oblatum 19-XII-1996 & 6-III-98 / Published online: 14 October 1998 1. Introduction Let k be a field of characteristic zero. We denote by M the Gro- thendieck ring of algebraic varieties over k (i.e. reduced separated schemes of finite type over k). It is the ring generated by symbols ?S?, for S an algebraic variety over k, with the relations ?S? ? ?S 0 ? if S is isomorphic to S 0 ; ?S? ? ?S n S 0 ? ? ?S 0 ? if S 0 is closed in S and ?S S 0 ? ? ?S??S 0 ?.

• ?s


• semi-algebraic condition


• over z


• variety over


• l?x ?


• let ‘


• ?w ?


• k??t??? ?