Grothendieck duality and base change / Brian Conrad.
By: Conrad, BrianMaterial type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1750.Publisher: Berlin ; New York : Springer, ©2000Description: 1 online resource (296 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540400158; 354040015XSubject(s): Duality theory (Mathematics) | Schemes (Algebraic geometry) | Duality theory (Mathematics) | Schemes (Algebraic geometry) | Grothendieck-Dualität | Schema Mathematik | Dualité, Principe de | SchémasGenre/Form: Electronic books. Additional physical formats: Print version:: Grothendieck duality and base change.DDC classification: 510 s | 515/.782 LOC classification: QA3 | .L28 no. 1750 | QA564Online resources: Click here to access online
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Includes bibliographical references (pages 291-292) and index.
Introduction -- Basic compatibilities -- Duality foundations -- Proof of main theorem.
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.