AI 中文总结
本研究确定特殊线性塔中相邻Stiefel纤维序列的两个跨阶段态射的性质，复实现可分类分裂二次曲面上的定向向量丛，并将结果用于给出投射模的分裂与生成准则。
AI 中文摘要
我们确定了特殊线性塔中源自相邻Stiefel纤维序列的两个跨阶段态射。在特征零域上，第一个在偶数阶段是Wood态射，在奇数阶段消失；第二个在偶数阶段由motivic Hopf元稳定诱导，在奇数阶段为零。复实现因此对分裂二次曲面$Q_{2n-1}$上$n\geq5$的定向秩$(n-2)$向量丛进行了分类。随后我们应用这些计算，给出了投射模的精确余秩二分裂和高效生成准则。
英文摘要
We determine the two cross-stage morphisms arising from adjacent Stiefel fiber sequences in the special linear tower. Over characteristic-zero fields, the first is the Wood morphism at even stages and vanishes at odd stages; the second is induced stably by the motivic Hopf element at even stages and is zero at odd stages. Complex realization consequently classifies oriented rank-$(n-2)$ vector bundles on the split quadric $Q_{2n-1}$ for $n\geq5$. We then apply these calculations to give exact corank-two splitting and efficient generation criteria for projective modules.
