发表机构
K. N. Toosi University of Technology（K.N.托伊西理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了线性约束 Kloosterman 族的顶权层的连通几何幺正群，通过四阶矩恒等式和射影射线论证，在无需有限群分类的情况下证明其为特殊线性群 SL_r(n)。
AI 中文摘要
我们确定了在每一维 n ≥ 4 和每一特征 p > max(2,n) 下，与线性约束 Kloosterman 族相伴的顶权层的连通几何幺正群。定量输入是一个四阶矩恒等式，其辅助几何依赖于矩的次数而非环境的族维数。在精确解耦后，一般层由 Cayley 三次曲面的平面截面控制，一个射影射线论证在每一固定维数中一致地给出所需的幂节省。在几何方面，局部 Fourier 变换计算和 Rojas-Leon 的乘法卷积公式产生一个非恒等幂幺边界元素。四阶矩、约化性、无限性和 Larsen 的替代定理随后给出 G_geom^0(W_n) = SL_r(n)，无需有限群分类或数值例外情形证书。作为比较，我们保留独立的 Guralnick-Tiep 路线，包括其六阶矩和精确有限计算，但主定理的证明中未使用该路线。
英文摘要
We determine the connected geometric monodromy of the top-weight sheaves attached to linearly constrained Kloosterman families in every dimension n >= 4 and every characteristic p > max(2,n). The quantitative input is a fourth-moment identity whose auxiliary geometry depends on the moment degree rather than on the ambient family dimension. After an exact decoupling, the generic stratum is controlled by plane sections of the Cayley cubic, and a projective-ray argument gives the required power saving uniformly in each fixed dimension. On the geometric side, a local Fourier-transform calculation and Rojas-Leon's multiplicative-convolution formula produce a nonidentity unipotent boundary element. The fourth moment, reductivity, infinitude, and Larsen's alternative then give G_geom^0(W_n) = SL_r(n) without finite-group classification or numerical exceptional-case certificates. For comparison, we retain the independent Guralnick-Tiep route, including its sixth-moment and exact finite computations, but it is not used in the proof of the main theorem.
Comments65 pages. The main theorem is independent of finite-group classification. An independent Guralnick-Tiep route is retained as a consistency check
