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Geometric motivic integration on Artin n-stacks

Balwe, Chetan T (2008) Geometric motivic integration on Artin n-stacks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Balwe, Chetan Tctb8@pitt.eduCTB8
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairHales, Thomas C.hales@pitt.eduHALES
Committee MemberIon, Bogdanbion@pitt.eduBION
Committee MemberAvigad,
Committee MemberGartside, Paulgartside@math.pitt.eduPMG20
Date: 29 October 2008
Date Type: Completion
Defense Date: 17 April 2008
Approval Date: 29 October 2008
Submission Date: 1 July 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: algebraic geometry; arc spaces; motivic integration; stacks
Other ID:, etd-07012008-134727
Date Deposited: 10 Nov 2011 19:49
Last Modified: 15 Nov 2016 13:45


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