@inbook{43e42faccd9f4c09b93cd44c308b08e9,

title = "The stable Galois correspondence for real closed fields",

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: SHG → SHk from the G-equivariant stable homotopy category to the stable motivic homotopy category over k such that c#x002a;L/k (G/H+) = Spec(LH)+. 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{\textquoteright}s theorem on the (2, η)- periodic stable motivic homotopy category and an isomorphism range for the map (formula presented) induced by C2-equivariant Betti realization.",

keywords = "Equivariant Betti realization, Equivariant and motivic stable homotopy theory",

author = "J. Heller and K. Ormsby",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

doi = "10.1090/conm/707/14250",

language = "English (US)",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "1--9",

booktitle = "Contemporary Mathematics",

address = "United States",

}