Algebraic De Rham cohomology
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- Hartshorne, R. Manuscripta Math (1972) 7: 125. doi:10.1007/BF01679709
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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.