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Since its conception by Kontsevich in 1995, the
technique of motivic integration has found numerous
applications in algebraic geometry and representation
theory. The work of Denef, Loeser and Cluckers led to
the formulation of different versions of motivic
integration geometric motivic integration,
arithmetic motivic integration and the theory of constructible motivic functions . This book
addresses the problem of generalizing the theory
geometric motivic integration to Artin n-stacks. We
follow the construction of higher Artin stacks as
proposed by Toen and Vezzosi. A brief review of this
construction along with some of the basic notions of
homotopical algebra is also provided. Applications of
the theory of motivic integration on varieties have
been very fruitful and this work should pave the way
for similar results for Artin stacks. Also, some of
these ideas may prove useful in generalizing other
versions of motivic integration to Artin stacks.
technique of motivic integration has found numerous
applications in algebraic geometry and representation
theory. The work of Denef, Loeser and Cluckers led to
the formulation of different versions of motivic
integration geometric motivic integration,
arithmetic motivic integration and the theory of constructible motivic functions . This book
addresses the problem of generalizing the theory
geometric motivic integration to Artin n-stacks. We
follow the construction of higher Artin stacks as
proposed by Toen and Vezzosi. A brief review of this
construction along with some of the basic notions of
homotopical algebra is also provided. Applications of
the theory of motivic integration on varieties have
been very fruitful and this work should pave the way
for similar results for Artin stacks. Also, some of
these ideas may prove useful in generalizing other
versions of motivic integration to Artin stacks.