Motivic concentration theorem

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.

Publication year:2020

Keywords:Cyclic Homology, Categories, Formula

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BOF-publication weight:1

CSS-citation score:1

Authors:International

Authors from:Higher Education

Accessibility:Closed