The Levelwise Finite Generation of Free Tambara Functors

Emory Sun

The Levelwise Finite Generation of Free Tambara Functors

Group Theory 2025-11-04 v3 Commutative Algebra Algebraic Topology

Authors: Emory Sun

Abstract

We prove the levelwise finite generation of free polynomial $G$ -Tambara functors in a collection of cases, most notably when $G$ is a finite Dedekind group or when $G \cong C_p \rtimes C_q$ , $p > q$ primes. In the process, we establish the permanence of various finiteness conditions under box products and norms $n_H^G$ of Tambara functors, including a weak Hilbert Basis Theorem.

Keywords

Tambara functors levelwise finite generation Dedekind group box products norms Hilbert Basis Theorem finite groups

Cite

@article{arxiv.2508.08340,
  title  = {The Levelwise Finite Generation of Free Tambara Functors},
  author = {Emory Sun},
  journal= {arXiv preprint arXiv:2508.08340},
  year   = {2025}
}

Comments

33 pages; v2: fixed minor typos, added affiliation and email v3: improved exposition, fixed more typos

The Levelwise Finite Generation of Free Tambara Functors

Abstract

Keywords

Cite

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