2011/08/24 by J. P. C. Greenlees, Greenlees, J. P. C.
Mathematics · #55N91 #55P42 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N91 #msc:55P42
paper · pdf · doi:10.48550/arxiv.1108.4868
arxiv created 2011/08/24 · openalex publication_date 2011/08/24 · arxiv updated 2011/08/25 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In previous work it is shown that there is an abelian category A(G) constructed to model rational G-equivariant cohomology theories, where G is a torus of rank r together with a homology functor \piA_* : Gspectra ---> A(G), and an Adams spectral sequence ExtA (G) (\piA_*(X), \piA_*(Y)) ===> [X,Y]G_* In joint work with Shipley (arxiv:1101.2511), it is shown that the Adams spectral sequence can be lifted to a Quillen equivalence Rational-Gspectra = DG-A (G). The purpose of the present paper is to prove that A(G) has injective dimension precisely r, and to construct certain torsion functors allowing us to make certain right adjoint constructions (such as products) in A(G). Along the way, we have an opportunity to prove a flatness result, and describe algebraic counterparts of some basic change of groups adjunctions.