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100   $a20121227d2000      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aGrothendieck Duality and Base Change$b[electronic resource] /$fby Brian Conrad
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (XII, 300 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1750
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-41134-8 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Basic compatibilities -- Duality foundations -- Proof of main theorom -- Examples: Higher direct images. Curves -- Residues and cohomology with supports -- Trace map on smooth curves.
330   $aGrothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1750
606   $aAlgebraic geometry
606   $aNumber theory
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aAlgebraic geometry.
615  0$aNumber theory.
615 14$aAlgebraic Geometry.
615 24$aNumber Theory.
676   $a515/.782
700   $aConrad$b Brian$4aut$4http://id.loc.gov/vocabulary/relators/aut$065658
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466670603316
996   $aGrothendieck duality and base change$9378457
997   $aUNISA