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Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Grothendieck Duality and Base Change ([EBook] /) / edited by Brian Conrad.
Added Personal Name	Conrad, Brian editor.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2000.
Physical Details	XII, 300 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1750
ISBN	9783540400158
Summary Note	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.:
Contents note	Introduction -- Basic compatibilities -- Duality foundations -- Proof of main theorom -- Examples: Higher direct images. Curves -- Residues and cohomology with supports -- Trace map on smooth curves.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b75857
Links to Related Works	Subject References: Algebraic Geometry . Mathematics . Number Theory . Authors: Conrad, Brian . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 516.35 .

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Grothendieck Duality and Base Change

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