Galois equivariance and stable motivic homotopy theory

By J. Heller, K. Ormsby. 2014

51 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/84ce907c4c776508cb9bdf067f184388f9f3b4ec

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Citations in the corpus

The first stable homotopy groups of motivic spheres (2016, background): “2) vastly generalizes computations in [51] for fields of cohomological dimension at most two, and in [13] and [20] for the real numbers.”
Norms in motivic homotopy theory (2017, methodology): “ Sis the spectrum of a eld kand p: G!His a nite quotient corresponding to a nite Galois extension L=k, the composition SH(BH) p ! SH(BG) !SH(k) is the functor c L=k introduced by Heller and Ormsby in [HO16], building on earlier work of Hu [Hu01, x3]. 10.1. The pronite etale fundamental groupoid. We ”