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Title: | Motivic concentration theorem | Authors: | Tabuada, Goncalo VAN DEN BERGH, Michel |
Issue Date: | 2020 | Publisher: | INT PRESS BOSTON, INC | Source: | MATHEMATICAL RESEARCH LETTERS, 27 (2) , p. 565 -589 | Abstract: | In this short article, given a smooth diagonalizable group scheme G of finite type acting on a smooth quasi-compact separated scheme X, we prove that (after inverting some elements of representation ring of G) all the information concerning the additive invariants of the quotient stack [X/G] is "concentrated" in the subscheme of G-fixed points X-G. Moreover, in the particular case where G is connected and the action has finite stabilizers, we compute the additive invariants of [X/G] using solely the subgroups of roots of unity of G. As an application, we establish a Lefschtez-Riemann-Roch formula for the computation of the additive invariants of proper push-forwards. | Notes: | Tabuada, G (corresponding author), MIT, Dept Math, Cambridge, MA 02139 USA.; Tabuada, G (corresponding author), FCT UNL, Dept Matemat, Lisbon, Portugal.; Tabuada, G (corresponding author), FCT UNL, Ctr Matemat & Aplicacoes CMA, Lisbon, Portugal. tabuada@math.mit.edu; michel.vandenbergh@uhasselt.be |
Other: | Tabuada, G (corresponding author), MIT, Dept Math, Cambridge, MA 02139 USA; FCT UNL, Dept Matemat, Lisbon, Portugal; FCT UNL, Ctr Matemat & Aplicacoes CMA, Lisbon, Portugal. tabuada@math.mit.edu; michel.vandenbergh@uhasselt.be | Keywords: | Cyclic Homology;Categories;Formula | Document URI: | http://hdl.handle.net/1942/31800 | Link to publication/dataset: | https://dx.doi.org/10.4310/MRL.2020.v27.n2.a10 | ISSN: | 1073-2780 | e-ISSN: | 1945-001X | ISI #: | WOS:000540233200010 | Rights: | by International Press of Boston, Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2021 |
Appears in Collections: | Research publications |
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