Rational Torus-equivariant Stable Homotopy Ii: the Algebra of Localization and Inflation
نویسنده
چکیده
In [5] we constructed an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and showed it can be used as the basis of a finite Adams spectral sequence for calculating groups of stable G-maps. In the present paper we make an algebraic study of the category A(G). We show how to separate information from isotropy groups with the same identity component, giving an equivalent category A(G) that is often easier to work with. In particular, we prove A(G) has injective dimension equal to the rank of G, and explain how to view it as a category of modules over a ring R with many objects, in preparation for [6].
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تاریخ انتشار 2007