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October 20, 2025Open Access

Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic

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This paper shows non-noetherian property in commutative algebra of polynomial functors, indicating implications for representation stability.

The main finding is that the algebra of polarizations is not noetherian, highlighting a key failure in representation stability.
Key evidence shows that the p-th power of every multisymmetric polynomial belongs to the algebra P, showcasing a central technical result.
Observational analysis considers properties of the ring of multisymmetric polynomials, revealing the non-noetherian nature of P.
This signifies a broader implication in invariant theory and representation stability, suggesting further inquiries into polynomial structures.

Karthik Ganapathy (2025) studied this question.

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This paper shows non-noetherian property in commutative algebra of polynomial functors, indicating implications for representation stability.