  In this paper we adapt the notion of the nucleus defined by Benson, Carlson,
and Robinson to compact Lie groups in non-modular characteristic. We show that
it describes the singularities of the projective scheme of the cohomology of
its classifying space. A notion of support for singularity categories of ring
spectra (in the sense of Greenlees and Stevenson) is established, and is shown
to be precisely the nucleus in this case, consistent with a conjecture of
Benson and Greenlees for finite groups.
