On the motivic spectral sequence

Abstract

It is shown that the Grayson tower for $K$-theory of smooth algebraic varieties is isomorphic to the slice tower of $S^1$-spectra. We also extend the Grayson tower to bispectra and show that the Grayson motivic spectral sequence is isomorphic to the motivic spectral sequence produced by the Voevodsky slice tower for the motivic $K$-theory spectrum $KGL$. This solves Suslin's problem for these two spectral sequences in the affirmative.

This is the final revised version

References in corpus (1)

• Algebraic K-theory, A^1-homotopy and Riemann-Roch theorems

Cited by in corpus (3)

• The Generalized Slices of Hermitian K-Theory
• Reconstructing rational stable motivic homotopy theory
• Fibrant resolutions for motivic Thom spectra