论文标题
相对大多项式环
Relative big polynomial rings
论文作者
论文摘要
令$ k $为带有复杂系数的Laurent系列的领域，令$ \ Mathcal {r} $是标准级别的多项式环$ k [x_1，\ ldots，x_n] $的反限制，而让$ \ \ \ \ m nrycal {r}^ryments $ nounding nounding unding unding unding unding y Mathist $分母。在与Erman和Sam的以前的联合合作中，我们表明$ \ Mathcal {r} $和$ \ Mathcal {r}^{\ flat} $（以及许多类似定义的环）是抽象的多项式环，并将其用来提供Stillman猜想的新证明。在本文中，我们证明了补充结果，即$ \ Mathcal {r} $是$ \ Mathcal {r}^{\ flat} $的多项式代数。
Let $K$ be the field of Laurent series with complex coefficients, let $\mathcal{R}$ be the inverse limit of the standard-graded polynomial rings $K[x_1, \ldots, x_n]$, and let $\mathcal{R}^{\flat}$ be the subring of $\mathcal{R}$ consisting of elements with bounded denominators. In previous joint work with Erman and Sam, we showed that $\mathcal{R}$ and $\mathcal{R}^{\flat}$ (and many similarly defined rings) are abstractly polynomial rings, and used this to give new proofs of Stillman's conjecture. In this paper, we prove the complementary result that $\mathcal{R}$ is a polynomial algebra over $\mathcal{R}^{\flat}$.
