Geometric motivic integration on Artin n-stacks
We construct a measure on the Boolean algebra of sets of formal arcs on an Artin stack which are definable in the language of Denef-Pas. The measure takes its values in a ring that is obtained from the Grothendieck ring of Artin stacks over the residue field by a localization followed by a completion. This construction is analogous to the construction of motivic measure on varieties by Denef and Loeser. We also obtain a "change of base" formula which allows us to relate the motivic measure on different stacks.
Advisor:Professor Thomas C. Hales; Professor Bogdan Ion; Professor Jeremy Avigad; Professor Paul Gartside
School:University of Pittsburgh
School Location:USA - Pennsylvania
Source Type:Master's Thesis
Date of Publication:10/29/2008