We reinterpret algebraic de Rham cohomology for a possibly singular complex variety $X$ as sheaf cohomology in the site of smooth schemes over $X$ with Voevodsky’s $h$-topology. Our results extend to the algebraic de Rham complex as well. Our main technique is to extend Cech cohomology of hypercovers to arbitrary local acyclic fibrations of simplicial presheaves.
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机译：我们重新解释代数de Rham的同调性，将其表示为可能复杂的$ X $的奇异同系性，因为在Voevodsky的$ h $拓扑中，光滑的方案超过了$ X $。我们的结果也扩展到代数de Rham复合体。我们的主要技术是将超覆盖层的Cech同构性扩展到简单先滑轮的任意局部无环纤维化。
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