AI 中文总结
本文在特征零完美域上，针对连通分裂半单单连通群构造环面富集动机胞腔复形，通过多种理论关联与计算，实现了外尔复形与旗复形的插值并揭示高阶微分。
AI 中文摘要
布吕阿分解为分裂代数群、旗簇和极大紧群提供了胞腔模型，但动机边界保留了在旗商中丢失的定向性与环面平移数据。在特征为零的完美域上，设群为连通、分裂、半单且单连通的；固定一个具有分裂极大环面和幂么根基的博雷尔子群，我们为基本仿射空间构造了一个环面富集的动机胞腔复形，并计算了其各次度的边界。布吕阿序中的每个覆盖贡献一个由迁移余根、尾行列式权重及显式米尔诺-维特标架次数确定的二面算子。博特-萨梅尔森纯性证明了该公式，而幂么挠子将此复形与群的复形等同。在实数域上，实现函子在链层上将其与极大紧子群的外尔复形等同，同时环面增广给出旗复形。因此，单个动机复形在两种关联理论之间起到了插值作用；有限环面支撑滤化使这一点明确，在2可逆后，它通过实分裂环面的分支群特征标分裂，且支撑谱序列退化。对秩3特殊线性群与例外秩2情形的计算，展示了超出已知范围的首批高阶微分。
英文摘要
Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation data lost in the flag quotient. Over a perfect field of characteristic zero, let the group be connected, split, semisimple, and simply connected. Fixing a Borel subgroup with split maximal torus and unipotent radical, we construct a torus-enriched motivic cellular complex for the basic affine space and compute its boundary in every degree. Each cover in Bruhat order contributes a two-face operator determined by a transported coroot, a tail determinant weight, and an explicit Milnor--Witt frame degree. Bott--Samelson purity proves the formula, while the unipotent torsor identifies the complex with that of the group. Over the real numbers, realization identifies it at chain level with the extended-Weyl complex of a maximal compact subgroup, while torus augmentation gives the flag complex. A single motivic complex therefore interpolates between the two incidence theories. A finite torus-support filtration makes this explicit; after inversion of two it splits by the characters of the component group of the real split torus, and the support spectral sequence degenerates. Calculations in the rank-three special linear and exceptional rank-two cases exhibit the first higher differentials beyond the previously known range.
