Slices of motivic Landweber spectra

TL;DR

This paper explores the implications of Voevodsky's conjecture on the slices of algebraic cobordism spectrum MGL for motivic Landweber spectra, potentially simplifying the computation of slices of algebraic K-theory spectrum KGL.

Contribution

It demonstrates that Voevodsky's conjecture implies a general statement about slices of motivic Landweber spectra, supporting a proposed approach for computing KGL slices.

Findings

Voevodsky's conjecture implies a general statement about motivic Landweber spectra slices.

Supports the approach for computing KGL slices via Conner-Floyd isomorphism.

Confirms similar results announced by Hopkins-Morel.

Abstract

We show that the Conjecture of Voevodsky concerning slices of the algebraic cobordism spectrum MGL implies a general statement about the slices of motivic Landweber spectra. In particular it confirms the possible approach suggested by Voevodsky for the computation of the slices of the homotopy algebraic K-theory spectrum KGL via a Conner-Floyd isomorphism complementing Levine's unconditional proof of these slices over perfect fields. A similar result, and Voevodsky's conjecture over fields of char. 0, are also announced by Hopkins-Morel.