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arXiv · 2005.10147

On the rational motivic homotopy category

Frédéric Déglise·Jean Fasel·Adeel A. Khan·Fangzhou Jin
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Abstract

We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and Grothendieck-Verdier duality for SH_Q. Next, we prove that SH_Q is canonically SL-oriented; we compare SH_Q with the category of rational Milnor-Witt motives; and we relate the rational bivariant A^1-theory to Chow-Witt groups. These results are derived from analogous statements for the minus part of SH[1/2].

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Frédéric Déglise, Jean Fasel, Adeel A. Khan, Fangzhou Jin. 2020-05-20. On the rational motivic homotopy category. https://doi.org/10.5802/jep.153

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