Galois equivariance and stable motivic homotopy theory

J. Heller, K. Ormsby

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)8047-8077
Number of pages31
JournalTransactions of the American Mathematical Society
Issue number11
StatePublished - 2016


  • Equivariant Betti realization
  • Equivariant and motivic stable homotopy theory

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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