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ON THE MOTIVIC SPECTRAL SEQUENCE

Part of: Spectral sequences $K$-theory in geometry

Published online by Cambridge University Press:  25 November 2015

Grigory Garkusha  and
Ivan Panin
Grigory Garkusha
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK (g.garkusha@swansea.ac.uk)URL: http://math.swansea.ac.uk/staff/gg/
Ivan Panin
Affiliation:
St. Petersburg Branch of V. A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia St. Petersburg State University, Department of Mathematics and Mechanics, Universitetsky prospekt, 28, 198504, Peterhof, St. Petersburg, Russia (paniniv@gmail.com)
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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.

Keywords

Motivic spectral sequencealgebraic K-theorymotivic cohomology

MSC classification

Primary: 19E08: $K$-theory of schemes 55T99: None of the above, but in this section
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 1 , February 2018 , pp. 137 - 170
Copyright
© Cambridge University Press 2015 

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