ON THE MOTIVIC SPECTRAL SEQUENCE. (25th November 2015)

• Record Type: Journal Article
• Authors: Garkusha, Grigory; Panin, Ivan
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 17:Number 1(2018)
• Page Start: 137
• Page End: 170
• Publication Date: 2015-11-25
• Subjects: 19E08, -- 55T99; Motivic spectral sequence, -- algebraic K-theory, -- motivic cohomology; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748015000419
• Languages: English
• ISSNs: 1474-7480

Abstract

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 $\mathit{KGL}$ . This solves Suslin's problem about these two spectral sequences in the affirmative.