On the rational motivic homotopy category

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].

arXiv comment53 pages, final version; to appear in Journal de l'École polytechnique

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Cited by in corpus (6)

• Fundamental classes in motivic homotopy theory
• Absolute Poincaré duality in étale cohomology
• On some finiteness results in real étale cohomology
• From Six Functors Formalisms to Derived Motivic Measures
• The geometric diagonal of the special linear algebraic cobordism
• Trace maps in motivic homotopy and local terms