Shortcuts
Please wait while page loads.
SISSA Library . Default .
PageMenu- Main Menu-
Page content

Catalogue Display

Lectures on Vanishing Theorems

Lectures on Vanishing Theorems
Catalogue Information
Field name Details
Dewey Class 500
Title Lectures on Vanishing Theorems ([EBook]) / by Hélène Esnault, Eckart Viehweg.
Author Esnault, Hélène. , 1953-
Added Personal Name Viehweg, Eckart
Other name(s) SpringerLink (Online service)
Publication Basel : Birkhäuser , 1992.
Physical Details VIII, 166 pages : online resource.
Series DMV Seminar ; 20
ISBN 9783034886000
Summary Note 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).:
Contents note § 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-0348-8600-0
Links to Related Works
Subject References:
Authors:
Corporate Authors:
Series:
Classification:
Catalogue Information 42166 Beginning of record . Catalogue Information 42166 Top of page .

Reviews


This item has not been rated.    Add a Review and/or Rating42166
. E-mail This Page
Quick Search