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.
Borghesi, S. (2003). Algebraic Morava K-theories. INVENTIONES MATHEMATICAE, 151(2), 381-413 [10.1007/s00222-002-0257-4].
Algebraic Morava K-theories
BORGHESI, SIMONE
2003
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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