Motivic concentration theorem

Gonçalo Tabuada, Michel van den Bergh

Research output: Contribution to journalArticlepeer-review


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 XG. 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.

Original languageEnglish
Pages (from-to)565-589
Number of pages25
JournalMathematical Research Letters
Issue number2
Publication statusPublished - 2020


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