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Grothendieck Duality and Base Change : Lecture Notes in Mathematics - Brian Conrad

Grothendieck Duality and Base Change

Lecture Notes in Mathematics

Paperback

Published: January 2001
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Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.

Introductionp. 1
Basic Compatibilitiesp. 21
Duality Foundationsp. 105
Proof of Main Theoremp. 175
Examplesp. 217
Residues and Cohomology with Supportsp. 237
Trace Map on Smooth Curvesp. 271
Bibliographyp. 291
Indexp. 293
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540411345
ISBN-10: 3540411348
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 300
Published: January 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.65
Weight (kg): 0.44