L. Gaunce Lewis
Syracuse
This is joint work with Florian Luca.
Let G be a compact Lie group, R be a commutative G-Mackey functor ring, and R(G) be the value of R at G. There is a topology on the set Spec(R) of Mackey functor prime ideals of R which is an obvious generalization of the Zariski topology on the spectrum of an ordinary commutative ring. This space Spec(R) carries a significant of information about R. In particular, the spectrum Spec(R(G)) of the ordinary commutative ring R(G) is a retract of Spec(R). Moreover, there is a function from the set Spec(R) to the set Conj(G) of conjugacy classes of subgroups of G, which can be used to determine the strongest possible induction theory satisfied by R.
This talk will be devoted to a discussion of the properties of Spec(R). Examples of Spec(R) for various groups G and rings R will also be discussed.