Abstract.
For any prime q and positive integer t, we construct a spectrum k(t) in the stable homotopy category of schemes over a field k equipped with an embedding k↪ℂ. In classical homotopy theory, the ℂ realization of k(t) is known as Morava K-theory. The algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic Eilenberg-MacLane spectra, which are known to represent motivic cohomology in the stable homotopy category of schemes.
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Oblatum 26-XI-2001 & 5-VIII-2002¶Published online: 8 November 2002
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Borghesi, S. Algebraic Morava K-theories. Invent. math. 151, 381–413 (2003). https://doi.org/10.1007/s00222-002-0257-4
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DOI: https://doi.org/10.1007/s00222-002-0257-4