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Motivic homotopical Galois extensions. (English) Zbl 1423.55035

Summary: We establish a formal framework for Rognes’s homotopical Galois theory and adapt it to the context of motivic spaces and spectra. We discuss examples of Galois extensions between Eilenberg-MacLane motivic spectra and between the Hermitian and algebraic \(K\)-theory spectra.

MSC:

55U35 Abstract and axiomatic homotopy theory in algebraic topology
13B05 Galois theory and commutative ring extensions
14F42 Motivic cohomology; motivic homotopy theory
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
55P42 Stable homotopy theory, spectra
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