基于K理论和无穷拓扑理论的高阶Tate中心扩张
Higher Tate central extensions via K-theory and infinity-topos theory
摘要：
利用Tate向量丛给出了一类称为K理论空间层上torsor的几何对象的分类定理。这使我们能够提出一个非常自然和简单的，替代的方法，泰特中心扩展，这是经典的构造使用gerbe的行列式理论。我们使用语言的无穷拓扑作为理论框架，因为它有很好的发展，扩展的概念的群体，行动，和torsors，这使得有可能把层的K理论空间作为一个组对象的这种，并解释一个delooping定理在K理论作为一个分类定理torsors在它。
英文摘要：
We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central extension, which was classically constructed by using the gerbe of determinant theories. We use the language of infinity-topoi as the theoretical framework, since it has well-developed, extended notions of groups, actions, and torsors, which make it possible to regard the sheaf of K-theory spaces as a group object of such kind and to interpret a delooping theorem in K-theory as a classification theorem for torsors over it.
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