Convergence conjecture for the I(k)-completed slice tower

Let $k$ be a field of finite virtual $2$-cohomological dimension and finite $p$-cohomological dimension for every prime $p>2$. The $I(k)$-completed slice tower is the slice tower after completion with respect to the ideal $I(k)$ in the Grothendieck–Witt ring. Convergence conjecture for the I(k)-completed slice tower. The $I(k)$-completed slice tower is convergent.

This formulation is proposed for fields of finite virtual $2$-cohomological dimension, including fields such as $\mathbb R$, and finite cohomological dimension away from $2$. The paper presents it as a suggested extension after noting that the original convergence conjecture fails for some base fields; its resolution is not supplied in the excerpt.