On the Tambara Affine Line
David Chan, David Mehrle, J.D. Quigley, Ben Spitz, Danika Van Niel

TL;DR
This paper advances the understanding of Tambara functors by describing their Nakaoka spectra in relation to classical spectra, introducing a ghost construction, and exploring equivariant algebraic properties.
Contribution
It provides explicit descriptions of Nakaoka spectra for various Tambara functors and introduces a ghost construction to analyze their properties.
Findings
Nakaoka spectrum of fixed point Tambara functor equals GIT quotient of Zariski spectrum
Describes Nakaoka spectrum of complex representation ring Tambara functor over cyclic groups
Introduces ghost construction and computes Krull dimensions of Tambara functors
Abstract
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prime ideals in a Tambara functor. In this work, we continue the study of the Nakoaka spectra of Tambara functors. We describe, in terms of the Zariski spectra of ordinary commutative rings, the Nakaoka spectra of many Tambara functors. In particular: we identify the Nakaoka spectrum of the fixed point Tambara functor of any -ring with the GIT quotient of its classical Zariski spectrum; we describe the Nakaoka spectrum of the complex representation ring Tambara functor over a cyclic group of prime order ; we describe the affine line (the Nakaoka spectra of free Tambara functors on one generator) over a cyclic group of prime order in terms of the Zariski spectra of , , and…
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