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The Nisnevich motive of an algebraic stack

Utsav Choudhury, Neeraj Deshmukh and Amit Hogadi

Vol. 8 (2023), No. 2, 245–273
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
Authors
Utsav Choudhury
Statistics and Mathematics Unit
Indian Statistical Institute
Kolkata
India
Neeraj Deshmukh
Institute für Mathematik
Universität Zürich
Zürich
Switzerland
Amit Hogadi
Department of Mathematics
Indian Insititute of Science Education and Research
Pune
India