manuscripta mathematica

, Volume 7, Issue 2, pp 125-140

First online:

Algebraic De Rham cohomology

  • Robin HartshorneAffiliated withMathematics Department, Harvard University

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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.