The stable Galois correspondence for real closed fields

J. Heller, K. Ormsby

Research output: Chapter in Book/Report/Conference proceedingChapter

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’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.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages1-9
Number of pages9
DOIs
StatePublished - Jan 1 2018

Publication series

NameContemporary Mathematics
Volume707
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

    Heller, J., & Ormsby, K. (2018). The stable Galois correspondence for real closed fields. In Contemporary Mathematics (pp. 1-9). (Contemporary Mathematics; Vol. 707). American Mathematical Society. https://doi.org/10.1090/conm/707/14250