论文标题
$ \ Mathcal {vi} $，$ nil $ claped的不稳定代数及其中心
Presheaves on $\mathcal{VI}$, $nil$-closed unstable algebras and their centres
论文作者
论文摘要
由functor $ \ text {hom} _ {\ mathcal {k} {k} {k} \ text {f.g。。 $ \ Mathcal {vi} $是Henn-Lannes-Schwartz理论的有限维矢量空间和注射。在本文中，我们利用该理论从听到的意义上研究了一个$ nil $ claped的Noetherian不稳定代数。对于$ \ Mathcal {vi} $上的$ f $ a Presheaf，我们构造了一个编码$ f $的groupoid $ \ mathcal {g} _f $。然后，服用$ f：= \ text {hom} _ {\ mathcal {k} \ text {f.g。}}}（k，h^*（\ _））$，我们展示$ k $的中心是如何由相关的groupoid确定的。我们还对Adams-Wilkerson的第二个定理进行了概括，定义了$ h^*（w）$的子代数$ h^*（W）与中心相关的$ h^*（c）$ - comodule结构。对于$ k $积分，我们解释了该$ h^*（c）$ - comodule结构的原始元素的代数也取决于与$ \ text {hom} _ {\ Mathcal {k} {k} \ text {f.g。在此过程中，我们证明了原始元素的代数也是noe的。
A $nil$-closed, noetherian, unstable algebra $K$ over the Steenrod Algebra is determined, up to isomorphism, by the functor $\text{Hom}_{\mathcal{K}\text{f.g.}}(K,H^*(\_))$, which is a presheaf on the category $\mathcal{VI}$ of finite dimensional vector spaces and injections, by the theory of Henn-Lannes-Schwartz. In this article, we use this theory to study the centre, in the sense of Heard, of a $nil$-closed noetherian unstable algebra. For $F$ a presheaf on $\mathcal{VI}$, we construct a groupoid $\mathcal{G}_F$ which encodes $F$. Then, taking $F:=\text{Hom}_{\mathcal{K}\text{f.g.}}(K,H^*(\_))$, we show how the centre of $K$ is determined by the associated groupoid. We also give a generalisation of the second theorem of Adams-Wilkerson, defining sub-algebras $H^*(W)^\mathcal{G}$ of $H^*(W)$ for appropriate groupoids $\mathcal{G}$. There is a $H^*(C)$-comodule structure on $K$ that is associated with the centre. For $K$ integral, we explain how the algebra of primitive elements of this $H^*(C)$-comodule structure is also determined by the groupoid associated with $\text{Hom}_{\mathcal{K}\text{f.g.}}(K,H^*(\_))$. Along the way, we prove that this algebra of primitive elements is also noetherian.
