Lectures on Vanishing Theorems / by Hélène Esnault, Eckart Viehweg
(DMV Seminar ; 20)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Birkhäuser Basel : Imprint: Birkhäuser |
| 出版年 | 1992 |
| 本文言語 | 英語 |
| 大きさ | VIII, 166 p : online resource |
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| 内容注記 | § 1 Kodaira’s vanishing theorem, a general discussion § 2 Logarithmic de Rham complexes § 3 Integral parts of Q-divisors and coverings § 4 Vanishing theorems, the formal set-up § 5 Vanishing theorems for invertible sheaves § 6 Differential forms and higher direct images § 7 Some applications of vanishing theorems § 8 Characteristic p methods: Lifting of schemes § 9 The Frobenius and its liftings § 10 The proof of Deligne and Illusie [12] § 11 Vanishing theorems in characteristic p § 12 Deformation theory for cohomology groups § 13 Generic vanishing theorems [26], [14] Appendix: Hypercohomology and spectral sequences References |
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| 一般注記 | 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 analytic and differential geometric methods beforehand. As a corollary of their methods M. Raynaud (loc. cit.) gave an easy proof of Kodaira vanishing in all characteristics, provided that X lifts to W2(k) |
| 著者標目 | *Esnault, Hélène author Viehweg, Eckart author SpringerLink (Online service) |
| 件 名 | LCSH:Science FREE:Science, general FREE:Science, general |
| 分 類 | DC23:500 |
| 巻冊次 | ISBN:9783034886000 
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| ISBN | 9783034886000 |
| URL | http://dx.doi.org/10.1007/978-3-0348-8600-0 |
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