C_2-equivariant stable homotopy from real motivic stable homotopy

Abstract

We give a method for computing the C_2-equivariant homotopy groups of the Betti realization of a p-complete cellular motivic spectrum over R in terms of its motivic homotopy groups. More generally, we show that Betti realization presents the C_2-equivariant p-complete stable homotopy category as a localization of the p-complete cellular real motivic stable homotopy category.

arXiv comment49 pages, 4 figures. v3: revisions based on comments from referee

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Cited by in corpus (11)

• On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra
• Real motivic and $C_2$-equivariant Mahowald invariants
• R-motivic stable stems
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory
• Topological models for stable motivic invariants of regular number rings
• $\mathbb{R}$-motivic $v_1$-periodic homotopy
• Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra
• An $\mathbb{R}$-motivic $v_1-$self-map of periodicity $1$
• The reduced ring of the $RO(C_2)$-graded $C_2$-equivariant stable stems
• Algebraicity in monochromatic homotopy theory
• The motivic lambda algebra and motivic Hopf invariant one problem