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arXiv · 2304.10631

On the Motivic Homotopy Type of Algebraic Stacks

Neeraj Deshmukh·Jack Hall
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Abstract

We construct smooth presentations of algebraic stacks that are local epimorphisms in the Morel-Voevodsky $\mathbb{A}^1$-homotopy category. As a consequence we show that the motive of a smooth stack (in Voevodsky's triangulated category of motives) has many of the same properties as the motive of a smooth scheme.

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Neeraj Deshmukh, Jack Hall. 2023-04-20. On the Motivic Homotopy Type of Algebraic Stacks. https://arxiv.org/abs/2304.10631

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