论文标题
多项式函子的拓扑成二：带有Noetherian Spectrum的基础环
Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum
论文作者
论文摘要
在上一篇论文中，第三作者证明了无限领域的有限程度多项式函子在拓扑上是诺瑟里亚人的。在本文中，我们证明了来自免费$ r $ r $模型的多项式函子，以有限生成的$ r $ $模型，对于任何spectrum spectrum是noetherian的交换ring $ r $。正如Erman-Sam-Snowden所指出的那样，当使用$ r = \ mathbb {z} $将其应用于对称权力总和时，Stillman的猜想证明之一是独立于特征性的。 我们的论文宣传并进一步开发了美丽但不是众所周知的多项式定律机制。特别是，对于任何有限生成的r模块，我们都将拓扑空间关联，当$ \ permatatorName {spec}（r）$ is is;这是我们对多项式函子的结果的零度情况。
In a previous paper, the third author proved that finite-degree polynomial functors over infinite fields are topologically Noetherian. In this paper, we prove that the same holds for polynomial functors from free $R$-modules to finitely generated $R$-modules, for any commutative ring $R$ whose spectrum is Noetherian. As Erman-Sam-Snowden pointed out, when applying this with $R = \mathbb{Z}$ to direct sums of symmetric powers, one of their proofs of a conjecture by Stillman becomes characteristic-independent. Our paper advertises and further develops the beautiful but not so well-known machinery of polynomial laws. In particular, to any finitely generated R-module M we associate a topological space, which we show is Noetherian when $\operatorname{Spec}(R)$ is; this is the degree-zero case of our result on polynomial functors.
