| 書目名稱 | Lectures on Vanishing Theorems | | 編輯 | Hélène Esnault,Eckart Viehweg | | 視頻video | http://file.papertrans.cn/584/583610/583610.mp4 | | 叢書名稱 | Oberwolfach Seminars | | 圖書封面 |  | | 描述 | Introduction M. Kodaira‘s vanishing theorem, saying that the inverse of an ample invert- ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre‘s GAGA-theorems [56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p > 0 some additional assumptions were needed. This was the state of the art until P. Deligne and 1. Illusie [12J proved the degeneration of the Hodge to de Rham spectral sequence for projective manifolds X defined over a field k of characteristic p > 0 and liftable to the second Witt vectors W2(k). Standard degeneration arguments allow to deduce the degeneration of the Hodge to de Rham spectral sequence in characteristic zero, as well, a re- sult which again could only be obtained by analyt | | 出版日期 | Book 1992 | | 關(guān)鍵詞 | Divisor; algebra; algebraic geometry; cohomology; deformation theory; manifold | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8600-0 | | isbn_softcover | 978-3-7643-2822-1 | | isbn_ebook | 978-3-0348-8600-0Series ISSN 1661-237X Series E-ISSN 2296-5041 | | issn_series | 1661-237X | | copyright | Springer Basel AG 1992 |
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