We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an essential way on several finiteness results for unramified cohomology.

中文翻译：

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代数群的一些有限性结果和高维域上的无分支上同调

我们制定并分析了高维域上线性代数群的几个有限性猜想。事实上，我们证明了代数环面以及其他一些情况下的所有这些猜想。这项工作在本质上依赖于非分枝上同调的几个有限性结果。