刚性阿代尔空间中有界高度子空间的联合等分布
Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
AI总结：
该研究证明了数域K上刚性阿代尔空间中有界高度d维K-子空间的联合等分布性，确定主常数、证明质量不逸出，给出一般数域下耦合的极限律，为相关等分布问题提供了关键结果。
AI中文摘要：
对于每个满足1≤d<n的情况，我们证明了当高度趋于无穷时，数域K上刚性阿代尔空间中d维K-子空间的联合等分布性，同时包含它们的阿基米德格拉斯曼像以及正规化子空间与商空间的K-线性等距类。我们确定了主常数，证明了质量不会从两个正规化因子中逸出，并得到了针对有界连续检验函数的全局等分布性。在一般数域上，两个正规化形状由行列式类关系耦合；在行列式类条件下，它们的极限律是对应纤维上哈尔诱导概率测度的乘积。
英文摘要：
For every $1\le d<n$, we prove joint equidistribution, as the height tends to infinity, of $d$-dimensional $K$-subspaces in a rigid adelic space over a number field $K$, together with their archimedean Grassmannian images and the $K$-linear isometry classes of the normalized subspace and quotient. We identify the leading constant, prove no escape of mass from either normalized factor, and obtain global equidistribution against bounded continuous test functions. Over a general number field, the two normalized shapes are coupled by a determinant-class relation; conditional on the determinant class, their limiting law is the product of the Haar-induced probability measures on the corresponding fibers.
