Motivic integration over Deligne-Mumford stacks
Abstract
Description
The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.
60 pages ; v.2, minor changes, references added ; v.3, a largely revised version. The base field is now assumed only to be perfect ; v.4, rewritten in detail. the set in which integrals take values is now the semiring of equivalence classes of convergent stacks. a result on the discrepancy of quotient stacks has been added; v.5, very slight modification. some historical accounts have been corrected
60 pages ; v.2, minor changes, references added ; v.3, a largely revised version. The base field is now assumed only to be perfect ; v.4, rewritten in detail. the set in which integrals take values is now the semiring of equivalence classes of convergent stacks. a result on the discrepancy of quotient stacks has been added; v.5, very slight modification. some historical accounts have been corrected