{"product_id":"9783764328221","title":"Oberwolfach Seminars","description":"\u003ch1\u003eOberwolfach Seminars\u003c\/h1\u003e \u003ch2\u003eEsnault; Vieweg\u003c\/h2\u003e \u003cp\u003eIntroduction 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 \u0026gt; 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p \u0026gt; 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 \u0026gt; 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).\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 1992-12-01\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783764328221\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-8600-0\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 166\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":46541643841676,"sku":"9783764328221","price":89.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783764328221.jpg?v=1775743422","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783764328221","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}