论文标题
扭曲的交换代数的光谱
The spectrum of a twisted commutative algebra
论文作者
论文摘要
扭曲的交换代数（对我们来说）是一个可交换的$ \ mathbf {q} $ - 配备了无限通用线性组的代数。在这样的代数中，“ $ \ mathbf {gl} $ - prime”理想承担了普通换向代数中的主要理想所履行的职责，因此了解它们至关重要。不幸的是，不同的$ \ mathbf {gl} $ - 素数可以具有相同的激进分子，这阻碍了一个几何研究。我们表明，可以通过使用超级向量空间来消除此问题：这样做提供了足够的几何形状来区分$ \ Mathbf {gl} $ - Primes。这产生了一种分析$ \ mathbf {gl} $ - 素数的有效方法。
A twisted commutative algebra is (for us) a commutative $\mathbf{Q}$-algebra equipped with an action of the infinite general linear group. In such algebras the "$\mathbf{GL}$-prime" ideals assume the duties fulfilled by prime ideals in ordinary commutative algebra, and so it is crucial to understand them. Unfortunately, distinct $\mathbf{GL}$-primes can have the same radical, which obstructs one from studying them geometrically. We show that this problem can be eliminated by working with super vector spaces: doing so provides enough geometry to distinguish $\mathbf{GL}$-primes. This yields an effective method for analyzing $\mathbf{GL}$-primes.
