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Motivic concentration theorem

Tijdschriftbijdrage - Tijdschriftartikel

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.
Tijdschrift: MATHEMATICAL RESEARCH LETTERS
ISSN: 1073-2780
Issue: 2
Volume: 27
Pagina's: 565 - 589
Jaar van publicatie:2020
Trefwoorden:Cyclic Homology, Categories, Formula
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:1
CSS-citation score:1
Auteurs:International
Authors from:Higher Education
Toegankelijkheid:Closed