发表机构
Indian Institute of Science Education and Research (IISER) Mohali（印度科学教育研究学院莫哈利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Tate截断函子保持motivic谱的连通性，并建立相应的Hurewicz定理和重构定理的切片类比。
AI 中文摘要
利用类似于Morel稳定连通性定理的方法，我们证明在任意域上，Tate截断函子$f_{0/n}$保持$S^1$-谱的motivic连通性。对于复形的一个类似结果，在完美域上给出了$L^{p,n}$-和$L_{bir}^n$-局部化的Hurewicz定理。在这些域上，我们为对应范畴建立了更强的连通性性质，表明当$\mathcal{C}$满足消去律时，$f_n^\mathcal{C}$保持具有$\mathcal{C}$-转移的motivic谱的连通性。然后我们利用motivic重构定理推导出$f_n$，从而$s_n$和$f_{0/n}$，也保持有效（进而$\mathbb{P}^1$-）motivic谱的连通性。在此过程中，我们还建立了motivic（有效）重构定理的切片类比，以及motivic $S^1$-和$\mathbb{P}^1$-识别定理的切片类比。
英文摘要
Using methods similar to Morel's stable connectivity theorem, we prove that, over an arbitrary field, the Tate truncation functors $f_{0/n}$ preserve motivic connectivity of $ S^1$-spectra. An analogous result for complexes yields a Hurewicz theorem for the $L^{p,n}$- and $L_{bir}^n$-localizations over perfect fields. Over such fields, we establish a stronger connectivity property for categories of correspondences, showing that $f_n^\mathcal{C}$ preserves connectivity of motivic spectra with $\mathcal{C}$-transfers, whenever $\mathcal{C}$ satisfies cancellation. We then use the motivic reconstruction theorem to deduce that $f_n$, and consequently $s_n$ and $f_{0/n}$, also preserve connectivity for effective (and thereby, $\mathbb{P}^1$-) motivic spectra. Along the way, we also establish the slice analog of the motivic (effective) reconstruction theorem, as well as the slice analog of motivic $S^1$- and $\mathbb{P}^1$-recognition theorems.
