### Abstract

In previous work [7], the authors constructed and studied a lift of the Galois correspondence to stable homotopy categories. In particular, if L/k is a finite Galois extension of fields with Galois group G, there is a functor c#x002a;_{L/k}: SH^{G} → SH_{k} from the G-equivariant stable homotopy category to the stable motivic homotopy category over k such that c#x002a;_{L/k} (G/H_{+}) = Spec(L^{H})+. The main theorem of [7] %citeHO:E2M says that when k is a real closed field and L = k[i], the restriction of c#x002a;_{L/k} to the η-complete subcategory is full and faithful. Here we “uncomplete” this theorem so that it applies to c#x002a;_{L/k} itself. Our main tools are Bachmann’s theorem on the (2, η)- periodic stable motivic homotopy category and an isomorphism range for the map (formula presented) induced by C_{2}-equivariant Betti realization.

Original language | English (US) |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 1-9 |

Number of pages | 9 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Contemporary Mathematics |
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Volume | 707 |

ISSN (Print) | 0271-4132 |

ISSN (Electronic) | 1098-3627 |

### Keywords

- Equivariant Betti realization
- Equivariant and motivic stable homotopy theory

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Contemporary Mathematics*(pp. 1-9). (Contemporary Mathematics; Vol. 707). American Mathematical Society. https://doi.org/10.1090/conm/707/14250