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Travaux de Gabber sur l'uniformisation locale et la cohomologie étale des schémas quasi-excellents
Authors: --- --- ---
ISSN: 03031179 ISBN: 9782856297902 Year: 2014 Publisher: Paris Société mathématique de France

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Gorenstein liaison, complete intersection liaison invariants and unobstructedness
Authors: --- ---
ISBN: 0821827383 Year: 2001 Publisher: Providence, R.I. American Mathematical Society

Algebraic geometry for associative algebras
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ISBN: 082470424X Year: 2000 Volume: 232 Publisher: New York ; Basel Marcel Dekker

Local cohomology and localization
Authors: --- ---
ISSN: 02693674 ISBN: 0582077672 047021595X 9780582077676 9780470215951 Year: 1989 Volume: 226 Publisher: Harlow: Longman scientific and technical,

Grothendieck duality and base change
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ISBN: 3540411348 354040015X 9783540411345 Year: 2000 Volume: 1750 Publisher: Berlin: Springer,

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Abstract

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.

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