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- catalog 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.".
- catalog contributor b11965134.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [291]-292) and index.".
- catalog description "Introduction -- Basic compatibilities -- Duality foundations -- Proof of main theorom -- Examples: Higher direct images. Curves -- Residues and cohomology with supports -- Trace map on smooth curves.".
- catalog extent "296 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540411348 (softcover : alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1750.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1750".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 515/.782 21".
- catalog subject "Duality theory (Mathematics)".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "Number theory.".
- catalog subject "QA3 .L28 no. 1750 QA564".
- catalog subject "Schemes (Algebraic geometry)".
- catalog tableOfContents "Introduction -- Basic compatibilities -- Duality foundations -- Proof of main theorom -- Examples: Higher direct images. Curves -- Residues and cohomology with supports -- Trace map on smooth curves.".
- catalog title "Grothendieck duality and base change / Brian Conrad.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".