Ananyevskiy, Alexey; Levine, Marc; Panin, Ivan Witt sheaves and the \(\eta\)-inverted sphere spectrum. (English) Zbl 1378.14021 J. Topol. 10, No. 2, 370-385 (2017). Summary: The first author [Ann. K-Theory 2, No. 4, 517–560 (2017; Zbl 1401.14117)] 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 of characteristic different from two. 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 and show that rationally this category is equivalent to the minus part of \(\mathcal{SH}(k)_{\mathbb{Q}}\). Cited in 1 ReviewCited in 15 Documents MSC: 14F42 Motivic cohomology; motivic homotopy theory 19G38 Hermitian \(K\)-theory, relations with \(K\)-theory of rings 55P42 Stable homotopy theory, spectra 11E81 Algebraic theory of quadratic forms; Witt groups and rings Citations:Zbl 1401.14117 PDFBibTeX XMLCite \textit{A. Ananyevskiy} et al., J. Topol. 10, No. 2, 370--385 (2017; Zbl 1378.14021) Full Text: DOI arXiv