论文标题
4倍分类的等效性
A 4-fold categorical equivalence
论文作者
论文摘要
在本说明中，我们将阐明Reineke所做的工作的一些直接后果，这些后果可能被证明在椭圆曲线的研究中很有用。特别是，我们将在平滑的投射曲线类别之间构建同构，并具有Quiver Grassmannians类别。我们将使用它来在一类Quiver Grassmannians，光滑的投射曲线，紧凑的Riemann表面和超越程度1的领域之间提供4倍的分类等效性。我们最后指出，椭圆曲线的类别是Quiver Grassmannians类别的同构，在其中为一类Quiver Grassmannians提供了分析组结构。
In this note, we will illuminate some immediate consequences of work done by Reineke that may prove to be useful in the study of elliptic curves. In particular, we will construct an isomorphism between the category of smooth projective curves with a category of quiver grassmannians. We will use this to provide a 4-fold categorical equivalence between a category of quiver grassmannians, smooth projective curves, compact Riemann surfaces and fields of transcendence degree 1 over $\mathbb{C}$. We finish with noting that the category of elliptic curves is isomorphic to a category of quiver grassmannians, whence providing an analytic group structure to a class of quiver grassmannians.
