English

The spectrum of the Burnside Tambara functor

Algebraic Topology 2026-01-30 v2 Commutative Algebra Group Theory

Abstract

We compute the spectrum of prime ideals in the Burnside Tambara functor over an arbitrary finite group. Our proof uses recent advances in the commutative algebra of Tambara functors, as well as a Tambara functor analogue of ghost coordinates which works over arbitrary finite groups and clarifies some previous computations. As examples, we explicitly compute the spectrum of the Burnside Tambara functor over all dihederal groups, the quaternion group Q8Q_8, the alternating group A4A_4, and the general linear group GL3(F2)GL_3(F_2).

Keywords

Cite

@article{arxiv.2506.10727,
  title  = {The spectrum of the Burnside Tambara functor},
  author = {Maxine Elena Calle and David Chan and David Mehrle and J. D. Quigley and Ben Spitz and Danika Van Niel},
  journal= {arXiv preprint arXiv:2506.10727},
  year   = {2026}
}

Comments

v2: Final version; to appear in International Mathematics Research Notices. v1: 22 pages, comments welcome!