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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 the motivic
cohomology agrees with the Chow groups of Edidin–Graham–Totaro with integer
coefficients.
Keywords
algebraic stacks, motives, motivic cohomology
Mathematical Subject Classification
Primary: 14F42
Milestones
Received: 10 August 2022
Revised: 19 January 2023
Accepted: 6 February 2023
Published: 14 June 2023
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