Abstract
We announce the development of a theory of algebraic De Rham cohomology and homology for arbitrary schemes over a field of characteristic zero. Over the complex numbers, this theory is equivalent to singular cohomology. Applications include generalizations of theorems of Lefschetz and Barth on the cohomology of projective varieties.
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Hartshorne, R. Algebraic De Rham cohomology. Manuscripta Math 7, 125–140 (1972). https://doi.org/10.1007/BF01679709
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DOI: https://doi.org/10.1007/BF01679709