论文标题
CDH血统的同型Hermitian $ K $ - 戒指理论
Cdh Descent for Homotopy Hermitian $K$-Theory of Rings with Involution
论文作者
论文摘要
我们为在r $中的$ \ frac {1} {2} \ in r $ in r $的戒指上分类了一个遗传矢量束的自动形态组的几何模型；这概括了schlichting-tripathi \ cite {schtri}的结果。然后，我们证明了Hermitian $ k $ - 理论的周期性定理，并使用它来构建$ e_ \ infty $ sotivic ring spectrum $ \ mathbf {kr}^{\ mathrm {alg}} $ shermitopy hermitian $ k $ - theory。从这些结果中，我们表明$ \ mathbf {kr}^{\ mathrm {alg}} $在基本变化下是稳定的，而同型Hermitian $ k $ k $ k $ k $ k $ k $ - 与之相关的cdh下降是正式的后果。
We provide a geometric model for the classifying space of automorphism groups of Hermitian vector bundles over a ring with involution $R$ such that $\frac{1}{2} \in R$; this generalizes a result of Schlichting-Tripathi \cite{SchTri}. We then prove a periodicity theorem for Hermitian $K$-theory and use it to construct an $E_\infty$ motivic ring spectrum $\mathbf{KR}^{\mathrm{alg}}$ representing homotopy Hermitian $K$-theory. From these results, we show that $\mathbf{KR}^{\mathrm{alg}}$ is stable under base change, and cdh descent for homotopy Hermitian $K$-theory of rings with involution is a formal consequence.
