TY - JOUR

T1 - Motivic concentration theorem

AU - Tabuada, Gonçalo

AU - van den Bergh, Michel

N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00297%2F2019/PT#
NSF CAREER Award #1350472
Sem PDF conforme despacho.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85091104630&partnerID=8YFLogxK

U2 - 10.4310/MRL.2020.v27.n2.a10

DO - 10.4310/MRL.2020.v27.n2.a10

M3 - Article

AN - SCOPUS:85091104630

VL - 27

SP - 565

EP - 589

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 2

ER -