References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt147",{id:"formSmash:upper:j_idt147",widgetVar:"widget_formSmash_upper_j_idt147",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt148_j_idt150",{id:"formSmash:upper:j_idt148:j_idt150",widgetVar:"widget_formSmash_upper_j_idt148_j_idt150",target:"formSmash:upper:j_idt148:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Destackification and Motivic Classes of StacksPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Department of Mathematics, Stockholm University , 2014. , 23 p.
##### Keyword [en]

Algebraic geometry, Algebraic stacks, Destackification, Grothendieck ring, Motive, Torus, Classifying stack
##### National Category

Geometry
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-107526ISBN: 978-91-7447-989-8OAI: oai:DiVA.org:su-107526DiVA: diva2:748075
##### Public defence

2014-10-24, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

##### List of papers

This thesis consists of three articles treating topics in the theory of algebraic stacks. The first two papers deal with motivic invariants. In the first, we show that the class of the classifying stack BPGL* _{n}* is the inverse of the class of PGL

In the second paper, we introduce an exponential function which can be viewed as a generalisation of Kapranov's motivic zeta function. We use this to derive a binomial theorem for a power operation defined on the Grothendieck ring of varieties. As an application, we give an explicit expression for the motivic class of a universal quasi-split torus, which generalises a result by Rökaeus.

The last paper treats destackification. We give an algorithm for removing stackiness from smooth, tame stacks with abelian stabilisers by repeatedly applying stacky blow-ups. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic zero, and to obtain a weak factorisation theorem for such stacks.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Manuscript.

Available from: 2014-10-02 Created: 2014-09-18 Last updated: 2014-10-30Bibliographically approved1. Motivic classes of some classifying stacks$(function(){PrimeFaces.cw("OverlayPanel","overlay748046",{id:"formSmash:j_idt437:0:j_idt441",widgetVar:"overlay748046",target:"formSmash:j_idt437:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. The Binomial Theorem and motivic classes of universal quasi-split tori$(function(){PrimeFaces.cw("OverlayPanel","overlay748049",{id:"formSmash:j_idt437:1:j_idt441",widgetVar:"overlay748049",target:"formSmash:j_idt437:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Functorial destackification of tame stacks with abelian stabilisers$(function(){PrimeFaces.cw("OverlayPanel","overlay748050",{id:"formSmash:j_idt437:2:j_idt441",widgetVar:"overlay748050",target:"formSmash:j_idt437:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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