Grothendieck Duality and Base Change, Issue 1750 (Google eBook)

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Springer Science & Business Media, Dec 12, 2000 - Mathematics - 296 pages
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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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Contents

I
1
II
5
III
7
IV
21
V
28
VI
32
VII
39
VIII
52
XVII
164
XVIII
175
XIX
182
XX
189
XXI
201
XXII
217
XXIII
225
XXIV
237

IX
56
X
76
XI
99
XII
105
XIII
125
XIV
133
XV
146
XVI
153
XXV
241
XXVI
271
XXVII
273
XXVIII
277
XXIX
283
XXX
291
XXXI
293
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