Galois equivariance and stable motivic homotopy theory

2015/02/11 by J. Heller, Jeremiah Heller, K. Ormsby +1 · 7 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · doi:10.1090/tran6647

Abstract

For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after completing at a prime and η (the motivic Hopf map) this results in a full and faithful embedding whenever k is real closed and L=k[i]. It is a full and faithful embedding after η-completion if a motivic version of Serre’s finiteness theorem is valid. We produce strong necessary conditions on the field extension L/k for this functor to be full and faithful. Along the way, we produce several results on the stable C₂-equivariant Betti realization functor and prove convergence theorems for the p-primary C₂-equivariant Adams spectral sequence.

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• Galois reconstruction of Artin-Tate ℝ-motivic spectra
• C₂-equivariant and R-motivic stable stems, II

Related

• Galois equivariance and stable motivic homotopy theory
• The stable Galois correspondence for real closed fields
• Motivic spectral Mackey functors
• Equivariant Motivic Homotopy Theory
• Motivic homotopy theory and stable homotopy groups