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Ananyevskiy 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. Thenπ  n    A   1(    S   k  −   )   ∗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    SH    (  k  )   Q    .

Witt sheaves and the η ‐inverted sphere spectrum