Rational torus-equivariant stable homotopy V: the torsion Adams spectral sequence

2021/10/01 by J. P. C. Greenlees, Greenlees, J. P. C.
Mathematics · #55N91 #55P42 #55P62 #55T15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2110.00268

openalex publication_date 2021/10/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, A_t(G) of finite injective dimension, a homology theory \piAt_* taking values in A_t(G) based on the homology of the Borel construction, and a finite Adams spectral sequence Ext_At(G)^*,*(\piAt_*(X), \piAt_*(Y)) ==> [X,Y]^G_* for rational G-spectra X and Y.

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