The Nisnevich Motive of an Algebraic Stack

The Nisnevich Motive of an Algebraic Stack

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...

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Veröffentlicht in:arXiv.org 2022-01
Hauptverfasser: Choudhury, Utsav, Deshmukh, Neeraj, Hogadi, Amit
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Homology
Mathematics - Algebraic Geometry
Mathematics - K-Theory and Homology
Quotients
Stacks
Topology
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2012.13304