Abstract
For G an arbitrary profinite group, we construct an algebraic model for rational Gspectra in terms of Gequivariant sheaves over the space of subgroups of G. This generalises the known case of finite groups to a much wider class of topological groups, and improves upon earlier work of the first author on the case where G is the padic integers.
As the purpose of an algebraic model is to allow one to use homological algebra to study questions of homotopy theory, we prove that the homological dimension (injective dimension) of the algebraic model is determined by the CantorBendixson rank of the space of closed subgroups of the profinite group G. This also provides a calculation of the homological dimension of the category of rational Mackey functors.
As the purpose of an algebraic model is to allow one to use homological algebra to study questions of homotopy theory, we prove that the homological dimension (injective dimension) of the algebraic model is determined by the CantorBendixson rank of the space of closed subgroups of the profinite group G. This also provides a calculation of the homological dimension of the category of rational Mackey functors.
Original language  English 

Journal  Algebraic and Geometric Topology 
Publication status  Accepted  18 Nov 2023 
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Rational Gspectra for profinite G
Author: Sugrue, D., Dec 2019Supervisor: Barnes, D. (Supervisor) & Mathieu, M. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy
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