论文标题
代数堆栈的分类Milnor广场和K理论
Categorical Milnor squares and K-theory of algebraic stacks
论文作者
论文摘要
我们介绍了一个稳定的$ \ infty $类别的米尔诺广场的概念，并证明了一个标准，在该标准下，代数K理论将这种广场发送到笛卡尔的Spectra Spectra。我们将其用于证明MILNOR切除和适当的切除定理，并在代数堆栈的K理论中具有仿射对角线和良好的稳定器。这得出了对这类堆栈的负K组消失的猜想的概括。
We introduce a notion of Milnor square of stable $\infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision theorems in the K-theory of algebraic stacks with affine diagonal and nice stabilizers. This yields a generalization of Weibel's conjecture on the vanishing of negative K-groups for this class of stacks.
