+612 9045 4394
 
CHECKOUT
Lectures on Vanishing Theorems : Agents and Actions Supplements - Helene Esnault

Lectures on Vanishing Theorems

Agents and Actions Supplements

Paperback Published: 1992
ISBN: 9783764328221
Number Of Pages: 166

Share This Book:

Paperback

$124.95
or 4 easy payments of $31.24 with Learn more
Ships in 5 to 9 business days

This book, an extended collection of lectures delivered at "Schloss Reisensburg" during the DMV-Seminar "Algebraic Geometry, 1991", aims at presenting Kodaira's vanishing theorem and several generalizations in a way which is as algebraic as possible. We develop the theory of logarithmic de Rham complexes, the use of the corresponding spectral sequence, lifting properties for manifolds and their Frobenius morphisms in characteristic p>0 and the proof of the degeneration of the Hodge to de Rham spectral sequence with algebraic methods, due to P. Deligne and L. Illusie. We apply those methods to obtain vanishing theorems. Several typical applications and the generic theorems of M. Green and R. Lazarsfeld complete the picture. This exposition is self-contained and accessible to anyone with background in modern algebraic geometry. The necessary formalisms from cohomology theory are recalled in an appendix. Contents: Introduction · Kodaira's vanishing theorem, a general discussion · Logarithmic de Rham complexes · Integral parts of Q-divisors and coverings · Vanishing theorems, the formal set-up · Vanishing theorems for invertible sheaves · Differential forms and higher direct images · Some applications of vanishing theorems · Characteristic p methods: Lifting of schemes · The Frobenius and its liftings · The proof of Deligne and Illusie · Vanishing theorems in characteristic p. · Deformation theory for cohomology groups · Generic vanishing theorems · Appendix: Hypercohomology and spectral sequences · References

x 1 Kodaira's vanishing theorem, a general discussion.- x 2 Logarithmic de Rham complexes.- x 3 Integral parts of Q-divisors and coverings.- x 4 Vanishing theorems, the formal set-up.- x 5 Vanishing theorems for invertible sheaves.- x 6 Differential forms and higher direct images.- x 7 Some applications of vanishing theorems.- x 8 Characteristic p methods: Lifting of schemes.- x 9 The Frobenius and its liftings.- x 10 The proof of Deligne and Illusie [12].- x 11 Vanishing theorems in characteristic p.- x 12 Deformation theory for cohomology groups.- x 13 Generic vanishing theorems [26], [14].- Appendix: Hypercohomology and spectral sequences.- References.

ISBN: 9783764328221
ISBN-10: 3764328223
Series: Agents and Actions Supplements
Audience: General
Format: Paperback
Language: English
Number Of Pages: 166
Published: 1992
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 24.41 x 16.99  x 0.97
Weight (kg): 0.29