论文标题
THH和TC（非常）远非同型函子
THH and TC are (very) far from being homotopy functors
论文作者
论文摘要
我们计算了几个方案的几个不变性的$ \ mathbb {a}^1 $ localiant，即拓扑hochschild同源性（$ \ mathrm {thh} $），拓扑环状同源性（$ \ mathrm {tc} $）和拓扑周期性的人物（$ \ matherology）（此过程非常残酷，并杀死了大多数不变性的完整版本。消失的陈述的主要成分是在积极特征中消失了$ \ mathbb {a}^1 $ - 局部 - de rham共同体（最终是结晶共同体）。
We compute the $\mathbb{A}^1$-localization of several invariants of schemes namely, topological Hochschild homology ($\mathrm{THH}$), topological cyclic homology ($\mathrm{TC}$) and topological periodic cyclic homology ($\mathrm{TP}$). This procedure is quite brutal and kills the completed versions of most of these invariants. The main ingredient for the vanishing statements is the vanishing of $\mathbb{A}^1$-localization of de Rham cohomology (and, eventually, crystalline cohomology) in positive characteristics.
