论文标题
整数的微不足道的纤维拓扑和框架动机
The trivial fiber topology and framed motives over the integers
论文作者
论文摘要
本文介绍了方案上的微不足道的纤维拓扑。对于一维的基础方案，我们使用它来描述稳定的动机同型类别和动机无限环路中的纤维替代品。我们还将garkusha-panin和voevodsky扩展到严格的$ \ mathbb {a}^{1} $ - 不变性定理到一维基方案。微不足道的纤维拓扑在动机同型类别的精制定位结果证明中起着核心作用。此外，我们扩展了Morel的$ \ Mathbb {A}^{1} $ - 稳定动机同型组的Nisnevich Sheaves上的连接定理。这些结果为对算术感兴趣的更深层基础方案的计算开辟了新的远景。
This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the Garkusha-Panin and Voevodsky strict $\mathbb{A}^{1}$-invariance theorems to one-dimensional base schemes. The trivial fiber topology plays a central role in the proof of refined localization results for motivic homotopy categories. Moreover, we extend Morel's $\mathbb{A}^{1}$-connectivity theorem on Nisnevich sheaves of stable motivic homotopy groups. These results open new vistas for computations of motivic invariants over deeper base schemes of arithmetic interest.
