Connectivity preservation for S^1-stable f_n and s_n

Prove that the colocalization functors f_n and the slice functors s_n preserve connectivity for motivic S^1-spectra, extending the established connectivity result for f_{0/n} beyond effective spectra.

Background

The paper proves connectivity preservation for f_{0/n} on motivic S1-spectra over arbitrary fields and for f_n, s_n, and f_{0/n} on effective spectra over perfect fields. The methods used for S1-spectra establish the result only for the localization f_{0/n}.

The authors explicitly state that neither of their two approaches extends to proving the corresponding connectivity result for f_n or s_n on S1-spectra. Establishing this would complete the connectivity theory for the full S1-stable slice filtration.

References

On the other hand, while the methods of \S2 do apply to $S1$-spectra (in fact, over all fields), they work only for $f_{0/n}$, not for $f_n$ or $s_n$. This is something we have not been able to achieve using either of the methods (\S2.4 and \S5.2) described in this paper.

— Connectivity of the slice filtration  (2609.34535 - Maity, 28 Sep 2026) in Section 6.2, final remark