English

The Nucleus of a Compact Lie Group, and Support of Singularity Categories

Algebraic Topology 2024-07-30 v2 Commutative Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.2405.00457,
  title  = {The Nucleus of a Compact Lie Group, and Support of Singularity Categories},
  author = {Thomas Peirce},
  journal= {arXiv preprint arXiv:2405.00457},
  year   = {2024}
}

Comments

Minor edits from reviewer comments