4
$\begingroup$

Voevodsky wrote on his paper "Open Problems in the Motivic Stable Homotopy Theory, 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 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?

Improve this question
$\endgroup$
1
  • 3
    $\begingroup$ Did you look at Voevodsky, Vladimir, "Open problems in the motivic stable homotopy theory". I. Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), 3–34, Int. Press Lect. Ser., 3, I, Int. Press, Somerville, MA, 2002 and at his "A possible new approach to the motivic spectral sequence for algebraic K-theory", Recent progress in homotopy theory (Baltimore, MD, 2000), 371–379, Contemp. Math., 293, Amer. Math. Soc., Providence, RI, 2002? $\endgroup$
    – Mikhail Bondarko
    Commented May 13, 2022 at 10:36

1 Answer 1

Reset to default
5
$\begingroup$

This is also investigated in Shane Kelly's thesis, see Section 4.2.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .