Voevodsky wrote on his paper "[Open Problems in the Motivic Stable Homotopy Theory,][1] I" that

> Three other groups of conjectures in motivic homotopy theory, not included in to this paper, seem to be slowly crystallizing. One group describes the behavior of slice filtration with respect to the functors $f^*$ ; $f_*$ ; $f^!$; $f_!$ for morphisms of different types. (page 5, page 3 on the pdf file)

However, appart from [Pelaez's paper][2] studying its behaviour with respect to $f^*$, I have been unable to find any reference for these conjectures.

My question is: **have these conjectures describing the functoriality of the slice filtration with respect to these functors been written anywhere?**

 


  [1]: https://www.math.ias.edu/vladimir/node/56
  [2]: https://www.cambridge.org/core/journals/journal-of-k-theory/article/abs/on-the-functoriality-of-the-slice-filtration/D95B64DE0BD7CDFE01E6E6C510CF8533