Witt sheaves and the $\eta$-inverted sphere spectrum

Abstract

Ananyevsky has recently computed the stable operations and cooperations of rational Witt theory. These computations enable us to show a motivic analog of Serre's finiteness result: Theorem: Let $k$ be a field. Then ${\pi }_n^{{\mathbb{A}}^1}({\mathbb{S}}_k^{-}{)}_{\ast }$ is torsion for $n>0$. As an application we define a category of Witt motives over $k$ and show that rationally this category is equivalent to the minus part of $SH(k{)}_{\mathbb{Q}}$.

16 pages

References in corpus (1)

• A comparison of motivic and classical homotopy theories

Cited by in corpus (7)

• Motivic and Real Etale Stable Homotopy Theory
• On the Conservativity of the Functor Assigning to a Motivic Spectrum its Motive
• Reconstructing rational stable motivic homotopy theory
• On the rational motivic homotopy category
• The eta-inverted sphere over the rationals
• Stable operations and cooperations in derived Witt theory with rational coefficients
• The geometric diagonal of the special linear algebraic cobordism