钻机类别上的稳定捆绑包
Stable bundles over rig categories
摘要：
证明了虚2-向量丛可由拓扑K理论的代数K理论K（ku）分类的猜想。因此，通过Ausoni和第四作者的工作，虚2-向量丛给我们提供了一个几何上同调理论，它具有与椭圆上同调相同的伸缩复杂性。主要的技术步骤是证明对于行为良好的小Rig范畴R（也称为双单范畴），与R相关联的环谱HR的代数K理论空间K（HR）等价于Z \times| BGL（R）|其中GL（R）是R上弱可逆矩阵的幺半范畴.如果π_0R是环，这几乎是形式的，我们的方法是用[BDRR 1]提供的环完备化版本代替R，其中π_0是π_0R的环完备化。
英文摘要：
The point of this paper is to prove the conjecture that virtual 2-vector bundles are classified by K(ku), the algebraic K-theory of topological K-theory. Hence, by the work of Ausoni and the fourth author, virtual 2-vector bundles give us a geometric cohomology theory of the same telescopic complexity as elliptic cohomology. The main technical step is showing that for well-behaved small rig categories R (also known as bimonoidal categories) the algebraic K-theory space, K(HR), of the ring spectrum HR associated to R is equivalent to Z \times |BGL(R)|^+, where GL(R) is the monoidal category of weakly invertible matrices over R. If π_0R is a ring this is almost formal, and our approach is to replace R by a ring completed version provided by [BDRR1] whose π_0 is the ring completion of π_0R.
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