| 書目名稱 | De Rham Cohomology of Differential Modules on Algebraic Varieties | | 編輯 | Yves André,Francesco Baldassarri | | 視頻video | http://file.papertrans.cn/264/263891/263891.mp4 | | 叢書名稱 | Progress in Mathematics | | 圖書封面 |  | | 描述 | This is a study of algebraic differential modules in several variables, and of some of their relations with analytic differential modules. Let us explain its source. The idea of computing the cohomology of a manifold, in particular its Betti numbers, by means of differential forms goes back to E. Cartan and G. De Rham. In the case of a smooth complex algebraic variety X, there are three variants: i) using the De Rham complex of algebraic differential forms on X, ii) using the De Rham complex of holomorphic differential forms on the analytic an manifold X underlying X, iii) using the De Rham complex of Coo complex differential forms on the differ- entiable manifold Xdlf underlying Xan. These variants tum out to be equivalent. Namely, one has canonical isomorphisms of hypercohomology: While the second isomorphism is a simple sheaf-theoretic consequence of the Poincare lemma, which identifies both vector spaces with the complex cohomology H (XtoP, C) of the topological space underlying X, the first isomorphism is a deeper result of A. Grothendieck, which shows in particular that the Betti numbers can be computed algebraically. This result has been generalized by P. Deligne to the case | | 出版日期 | Book 20011st edition | | 關(guān)鍵詞 | Dimension; Divisor; Geometrie; Grad; algebra; algebraic geometry; algebraic varieties | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8336-8 | | isbn_ebook | 978-3-0348-8336-8Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel AG 2001 |
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