Introduction to Grothendieck Duality Theory
- PDF / 9,660,402 Bytes
- 188 Pages / 504 x 720 pts Page_size
- 102 Downloads / 340 Views
146
Allen Altman University of California, La Jolla, CAIUSA
Steven Kleiman M.I.T., Dept. of Mathematics, Cambridge, MAIUSA
Introduction to Grothendieck Duality Theory
Springer-Verlag Berlin· Heidelberg· New York 1970
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under §54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
C by Springer-Vedag Berlin> Heidelberg 1970. library of Congress Catalog Card Number 71"1'2180 Printed lit Germany. Tide No. 330'
CONTENTS
Preface Chapter I
Study of
(lJX
1
Main Duality Results
2
Further discussion of
•••••••••.••••••••••.•.•.•
6
3
Differentials on Projective Space •••••••••...••••••.•
10
4
The Fundamental Local Isomorphism •.••••.•.•..•••••..•
12
Chapter II
5 (lJx·
Completions, Primary Decomposition and Length
1
Completions
15
2
Support of a Sheaf •••..•.•..••••..•••••••.•••••••••.•
24
3
Pr imary Decomposition
••••.•••••••.••.••••••••••••.••
26
4
Length and Characteristic Functions •••••.•.••••••••••
32
Chapter III
Depth and Dimension
38
1
Dimension Theory in Noetherian Rings •••••••••••••••••
2
Dimension Theory in Algebras of Finite Type over a Field 42
3
Depth
" •••. " .•..••. "........
46
4
Cohen-Macaulay Modules and Regular Local Rings •••••••
54
5
Homological Dimension
••••••••••••••••••••••••.••••••
58
Chapter IV
Duality Theorems
1
The Yoneda Pairing
••••••••••••••••••••••••••••••••••
67
2
The Spectral Sequence of a Composite Functor •.•••••••
3
Complements on
70 73
Extci (F ,G)
••.•......•.•...........•.
4
Serre Duality
•.•..
. . •. . . . . . . . . . .. . . . . . . .. . .. . . . . .
5
Grothendieck Duality
••••••••••••••.•••••••.••••..•••
Chapter V
Flat Morphisms
1
Faithful Flatness
2
Flat Morphisms
3
The Local Criterion of Flatness
4
Constructible Sets
5
Flat Morphisms and Open sets
................•.............•....
.....•...............................
82 86
••••••••••••••••••••••••
90 95 99
Differentials.......................................
102
Chapter VI 1
75 77
... .. " .... " " "
" " " " " " " " " "
.. " . " "
.
" " " "
.
Etale Morphisms
- 4 -
5
Quasifinite Morphisms Unramified Morphisms Etale Morphisms Morphisms
6
Cove rs ••••••••••••••••••••••••••••••••••••••••.•••••
2 3 4
..................................
Chapter VII
Generalities
2
Serre's criterion •••••••••••••.•.•••.•••••••••.•..•• D'ivisors Stability Differential Properties ••••••.•..•..••••••••..•..•• Algebraic Schemes ....•••.•..................•.....•
4
5 6
••.•.•••••••••••••••.•••••••••••••••.••
..........................................
Chapter VIII
115
119 122
Smooth Morphisms
1 3
110 112
128 136
142 147
15
Data Loading...
