Homology, Homotopy and Applications

Relations between slices and quotients of the algebraic cobordism spectrum

Markus Spitzweck

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Abstract

We prove a relative statement about the slices of the algebraic cobordism spectrum. If the map from MGL to a certain quotient of MGL introduced by Hopkins and Morel is the map to the zero-slice then a relative version of Voevodsky's conjecture on the slices of MGL holds true. We outline the picture for K-theory and rational slices.

Article information

Source
Homology Homotopy Appl., Volume 12, Number 2 (2010), 335-351.

Dates
First available in Project Euclid: 28 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296223886

Mathematical Reviews number (MathSciNet)
MR2771593

Zentralblatt MATH identifier
1209.14019

Subjects
Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15] 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 19E20: Relations with cohomology theories [See also 14Fxx]

Keywords
Slice algebraic cobordism spectrum K-theory

Citation

Spitzweck, Markus. Relations between slices and quotients of the algebraic cobordism spectrum. Homology Homotopy Appl. 12 (2010), no. 2, 335--351. https://projecteuclid.org/euclid.hha/1296223886


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