We prove that any finite-degree polynomial functor is topologically Noetherian. This theorem is motivated by the recent resolution of Stillman's conjecture and a recent Noetherianity proof for the space of cubics. Via work by Erman-Sam-Snowden, our theorem implies Stillman's conjecture and indeed boundedness of a wider class of invariants of ideals in polynomial rings with a fixed number of generators of prescribed degrees.

中文翻译：

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多项式函子的拓扑诺以太性

我们证明任何有限次多项式函子都是拓扑诺特的。这个定理是由斯蒂尔曼猜想的最近解决和最近关于立方空间的诺以太性证明推动的。通过 Erman-Sam-Snowden 的工作，我们的定理暗示了 Stillman 的猜想，实际上是多项式环中更广泛的理想不变量类的有界性，其中具有固定数量的规定度数的生成元。