Differential forms are a rich source of invariants in algebraic geometry. This approach was very successful for smooth varieties, but the singular case is less wellunderstood. We explain how the use of the h-topology (introduced by Suslin and Voevodsky in order to study motives) gives a very good object also in the singular case, at least in characteristic 0. We also explain problems and solutions in positive characteristic. Mathematics Subject Classification (2010). Primary 14-02; Secondary 14F10, 14J17, 14F20

中文翻译：

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代数几何中的微分形式——奇异情况下的新视角

微分形式是代数几何中不变量的丰富来源。这种方法对于平滑变体来说非常成功，但对于奇异的情况却不太了解。我们解释了 h 拓扑的使用（由 Suslin 和 Voevodsky 引入以研究动机）如何在奇异情况下也能给出一个很好的对象，至少在特征 0 中。我们还解释了正特征中的问题和解决方案。数学学科分类（2010）。小学 14-02; 次要 14F10、14J17、14F20