The Nisnevich Motive of an Algebraic Stack

Abstract

We construct the motive of an algebraic stack in the Nisnevich topology. For stacks which are Nisnevich locally quotient stacks, we give a presentation of the motive in terms of simplicial schemes. We also show that for quotient stacks the motivic cohomology agrees with the Edidin-Graham-Totaro Chow groups with integer coefficients.

20 pages. (v2) New section (Section 5) added on applications to motivic cohomology of stacks; (v3) minor changes

References in corpus (1)

• The motivic cobordism for group actions

Cited by in corpus (1)

• A motivic integral identity for $(-1)$-shifted symplectic stacks