dc.contributor.author Esnault, Hélène dc.contributor.author Viehweg, Eckart dc.date.accessioned 2016-09-23T14:50:26Z dc.date.available 2016-09-23T14:50:26Z dc.date.issued 1992 dc.identifier.isbn 978-3-7643-2822-1 dc.identifier.uri http://publications.mfo.de/handle/mfo/503 dc.description.abstract 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). en_US dc.language.iso en_US en_US dc.publisher Birkhäuser Basel en_US dc.relation.ispartofseries Oberwolfach Seminars;20 dc.title Lectures on vanishing theorems en_US dc.title.alternative DMV Seminar vol. 20 en_US dc.type Book en_US dc.identifier.doi 10.1007/978-3-0348-8600-0 local.series.id OWS-20
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