AI 中文总结
本文确定了整数上动机球面谱的第零积分Milnor-Witt茎，并建立了多种动机谱的细胞性及混合特征Dedekind域上的绝对纯性结果。
AI 中文摘要
主要结果确定了整数上的Morel-Voevodsky动机稳定同伦范畴中动机球面谱的第零积分Milnor-Witt茎。权重为零的分量是整数上非退化对称双线性形式的Grothendieck-Witt环。在此过程中，建立了各种动机谱（包括积分动机Eilenberg-MacLane谱）在任意域上的细胞性，以及混合特征Dedekind域上η-倒置动机球面谱的绝对纯性结果。
英文摘要
The main result determines the zeroth integral Milnor-Witt stem of the motivic sphere spectrum in the Morel-Voevodsky motivic stable homotopy category of the integers. The component in weight zero is the Grothendieck-Witt ring of nondegenerate symmetric bilinear forms over the integers. Along the way, cellularity of connective Witt theory, as well as an absolute purity result for the η-inverted motivic sphere spectrum, is established over Dedekind domains of mixed characteristic.
Comments25 pages, no figures, no AI. v2: Removed incorrect proof and the statements depending on it; main result is unchanged
