AI 中文总结
本文针对数域上半阿贝尔簇，在环面赋值为单临界且算术T-有效时，证明了一般等分布，建立了不同类型环面赋值的比较机制，进而得到对应Bogomolov定理。
AI 中文摘要
Kühne建立了半阿贝尔簇上典范阿德勒线丛的等分布，该情形不一定属于Yuan-Zhang定理的准典范范围。本文研究半阿贝尔簇紧化上的阿德勒线丛，其环面部分由环面赋值除子控制。主要的无条件结果为：当环面赋值是单临界且算术T-有效时的一般等分布。证明过程分离出Kühne论证中的渐近估计，并将其重新解释为沿显式压缩路径的估计，这为典范、准典范及更一般的环面赋值之间提供了比较机制。对于Bogomolov应用，准典范情形由Kühne的局部平凡化传输包处理。在为局部平凡化固定单一θ因子约定后，证明验证了Kühne操作下的Picard零θ因子，并通过准典范替换论证，得到本文所处理赋值类（单临界且算术T-有效环面赋值）对应的Bogomolov定理。
英文摘要
K{ü}hne established equidistribution for canonical adelic line bundles on semiabelian varieties, a setting which need not lie in the quasi-canonical range of Yuan-Zhang's theorem. We study adelic line bundles on semiabelian compactifications whose toric part is governed by a toric metrized divisor. The main unconditional result is generic equidistribution when the toric metric is monocritical and arithmetically T-effective. The proof isolates the asymptotic estimates in K{ü}hne's argument and reinterprets them as estimates along explicit compression paths. This gives a comparison mechanism between canonical, quasi-canonical, and more general toric metrics. For the Bogomolov application, the quasi-canonical case is handled by a K{ü}hne local-trivialization transport package. After fixing a single theta-factor convention for the local trivializations, the proof checks the Picard-zero theta factors under K{ü}hne's operations and obtains the Bogomolov theorem for the metric class treated in this paper, namely the monocritical and arithmetically T-effective toric metrics, through the quasi-canonical replacement argument.
Comments82 pages
