The Nisnevich Motive of an Algebraic Stack
Algebraic Geometry
2023-06-21 v3 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2012.13304,
title = {The Nisnevich Motive of an Algebraic Stack},
author = {Utsav Choudhury and Neeraj Deshmukh and Amit Hogadi},
journal= {arXiv preprint arXiv:2012.13304},
year = {2023}
}
Comments
20 pages. (v2) New section (Section 5) added on applications to motivic cohomology of stacks; (v3) minor changes