Commutative algebra with view toward algebraic geometry:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo
Springer
1999
|
| Edition: | 3. corrected printing |
| Series: | Graduate texts in mathematics
150 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 757 - 774 |
| Physical Description: | XVI, 797 S. 90 graph. Darst. |
| ISBN: | 3540942696 0387942696 0387942688 |
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MARC
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| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Eisenbud, David |d 1947- |e Verfasser |0 (DE-588)139999671 |4 aut | |
| 245 | 1 | 0 | |a Commutative algebra with view toward algebraic geometry |c David Eisenbud |
| 250 | |a 3. corrected printing | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo |b Springer |c 1999 | |
| 300 | |a XVI, 797 S. |b 90 graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 150 | |
| 500 | |a Literaturverz. S. 757 - 774 | ||
| 650 | 4 | |a Commutative algebra | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 150 |w (DE-604)BV000000067 |9 150 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912438&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016912438 | |
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| _version_ | 1807773507382149120 |
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CONTENTS
INTRODUCTION
1
ADVICE
FOR
THE
BEGINNER
.
2
INFORMATION
FOR
THE
EXPERT
.
2
PREREQUISITES
.
6
SOURCES
.
6
COURSES
.
7
A
FIRST
COURSE
.
7
A
SECOND
COURSE
.
8
ACKNOWLEDGEMENTS
.
.
9
0
ELEMENTARY
DEFINITIONS
11
0.1
RINGS
AND
IDEALS
.
11
0.2
UNIQUE
FACTORIZATION
.
13
0.3
MODULES
.
15
I
BASIC
CONSTRUCTIONS
19
1
ROOTS
OF
COMMUTATIVE
ALGEBRA
21
1.1
NUMBER
THEORY
.
21
1.2
ALGEBRAIC
CURVES
AND
FUNCTION
THEORY
.
23
1.3
INVARIANT
THEORY
.
24
1.4
THE
BASIS
THEOREM
.
27
1.4.1
FINITE
GENERATION
OF
INVARIANTS
.
29
VIII
CONTENTS
1.5
GRADED
RINGS
.
30
1.6
ALGEBRA
AND
GEOMETRY:
THE
NULLSTELLENSATZ
.
31
1.7
GEOMETRIC
INVARIANT
THEORY
.
37
1.8
PROJECTIVE
VARIETIES
.
39
1.9
HILBERT
FUNCTIONS
AND
POLYNOMIALS
.
42
1.10
FREE
RESOLUTIONS
AND
THE
SYZYGY
THEOREM
.
44
1.11
EXERCISES
.
46
NOETHERIAN
RINGS
AND
MODULES
.
46
AN
ANALYSIS
OF
HILBERT
'
S
FINITENESS
ARGUMENT
.
47
SOME
RINGS
OF
INVARIANTS
.
48
ALGEBRA
AND
GEOMETRY
.
49
GRADED
RINGS
AND
PROJECTIVE
GEOMETRY
.
52
HILBERT
FUNCTIONS
.
53
FREE
RESOLUTIONS
.
54
SPEC,
MAX-SPEC,
AND
THE
ZARISKI
TOPOLOGY
.
54
2
LOCALIZATION
57
2.1
FRACTIONS
.
59
2.2
HOM
AND
TENSOR
.
62
2.3
THE
CONSTRUCTION
OF
PRIMES
.
70
2.4
RINGS
AND
MODULES
OF
FINITE
LENGTH
.
71
2.5
PRODUCTS
OF
DOMAINS
.
78
2.6
EXERCISES
.
78
Z-GRADED
RINGS
AND
THEIR
LOCALIZATIONS
.
81
PARTITIONS
OF
UNITY
.
83
GLUING
.
83
CONSTRUCTING
PRIMES
.
84
IDEMPOTENTS,
PRODUCTS,
AND
CONNECTED
COMPONENTS
.
85
3
ASSOCIATED
PRIMES
AND
PRIMARY
DECOMPOSITION
87
3.1
ASSOCIATED
PRIMES
.
89
3.2
PRIME
AVOIDANCE
.
90
3.3
PRIMARY
DECOMPOSITION
.
94
3.4
PRIMARY
DECOMPOSITION
AND
FACTORIALITY
.
98
3.5
PRIMARY
DECOMPOSITION
IN
THE
GRADED
CASE
.
99
3.6
EXTRACTING
INFORMATION
FROM
PRIMARY
DECOMPOSITION
.
.
.
100
3.7
WHY
PRIMARY
DECOMPOSITION
IS
NOT
UNIQUE
.
102
3.8
GEOMETRIC
INTERPRETATION
OF
PRIMARY
DECOMPOSITION
.
103
3.9
SYMBOLIC
POWERS
AND
FUNCTIONS
VANISHING
TO
HIGH
ORDER
.
105
3.9.1
A
DETERMINANTAL
EXAMPLE
.
107
3.10
EXERCISES
.
109
GENERAL
GRADED
PRIMARY
DECOMPOSITION
.
110
PRIMARY
DECOMPOSITION
OF
MONOMIAL
IDEALS
.
ILL
THE
QUESTION
OF
UNIQUENESS
.
112
DETERMINANTAL
IDEALS
.
113
CONTENTS
IX
TOTAL
QUOTIENTS
.
113
PRIME
AVOIDANCE
.
114
4
INTEGRAL
DEPENDENCE
AND
THE
NULLSTELLENSATZ
117
4.1
THE
CAYLEY-HAMILTON
THEOREM
AND
NAKAYAMA
'
S
LEMMA
.
119
4.2
NORMAL
DOMAINS
AND
THE
NORMALIZATION
PROCESS
.
125
4.3
NORMALIZATION
IN
THE
ANALYTIC
CASE
.
128
4.4
PRIMES
IN
AN
INTEGRAL
EXTENSION
.
129
4.5
THE
NULLSTELLENSATZ
.
131
4.6
EXERCISES
.
135
NAKAYAMA
'
S
LEMMA
.
136
PROJECTIVE
MODULES
AND
LOCALLY
FREE
MODULES
.
136
INTEGRAL
CLOSURE
OF
IDEALS
.
137
NORMALIZATION
.
138
NORMALIZATION
AND
CONVEXITY
.
139
NULLSTELLENSATZ
.
142
THREE
MORE
PROOFS
OF
THE
NULLSTELLENSATZ
.
142
5
FILTRATIONS
AND
THE
ARTIN-REES
LEMMA
147
5.1
ASSOCIATED
GRADED
RINGS
AND
MODULES
.
148
5.2
THE
BLOWUP
ALGEBRA
.
150
5.3
THE
KRULL
INTERSECTION
THEOREM
.
152
5.4
THE
TANGENT
CONE
.
153
5.5
EXERCISES
.
154
6
FLAT
FAMILIES
157
6.1
ELEMENTARY
EXAMPLES
.
159
6.2
INTRODUCTION
TO
TOR
.
161
6.3
CRITERIA
FOR
FLATNESS
.
162
6.4
THE
LOCAL
CRITERION
FOR
FLATNESS
.
167
6.5
THE
REES
ALGEBRA
.
171
6.6
EXERCISES
.
172
FLAT
FAMILIES
OF
GRADED
MODULES
.
175
EMBEDDED
FIRST-ORDER
DEFORMATIONS
.
176
7
COMPLETIONS
AND
HENSEL
'
S
LEMMA
181
7.1
EXAMPLES
AND
DEFINITIONS
.
181
7.2
THE
UTILITY
OF
COMPLETIONS
.
184
7.3
LIFTING
IDEMPOTENTS
.
188
7.4
COHEN
STRUCTURE
THEORY
AND
COEFFICIENT
FIELDS
.
191
7.5
BASIC
PROPERTIES
OF
COMPLETION
.
194
7.6
MAPS
FROM
POWER
SERIES
RINGS
.
200
7.7
EXERCISES
.
205
MODULES
WHOSE
COMPLETIONS
ARE
ISOMORPHIC
.
205
THE
KRULL
TOPOLOGY
AND
CAUCHY
SEQUENCES
.
206
X
CONTENTS
COMPLETIONS
FROM
POWER
SERIES
.
207
COEFFICIENT
FIELDS
.
207
OTHER
VERSIONS
OF
HENSEL
'
S
LEMMA
.
208
II
DIMENSION
THEORY
213
8
INTRODUCTION
TO
DIMENSION
THEORY
215
8.1
AXIOMS
FOR
DIMENSION
.
220
8.2
OTHER
CHARACTERIZATIONS
OF
DIMENSION
.
222
8.2.1
AFFINE
RINGS
AND
NOETHER
NORMALIZATION
.
223
8.2.2
SYSTEMS
OF
PARAMETERS
AND
KRULL
'
S
PRINCIPAL
IDEAL
THEOREM
.
224
8.2.3
THE
DEGREE
OF
THE
HILBERT
POLYNOMIAL
.
225
9
FUNDAMENTAL
DEFINITIONS
OF
DIMENSION
THEORY
227
9.1
DIMENSION
ZERO
.
229
9.2
EXERCISES
.
230
10
THE
PRINCIPAL
IDEAL
THEOREM
AND
SYSTEMS
OF
PARAMETERS
233
10.1
SYSTEMS
OF
PARAMETERS
AND
IDEALS
OF
FINITE
COLENGTH
.
.
.
236
10.2
DIMENSION
OF
BASE
AND
FIBER
.
238
10.3
REGULAR
LOCAL
RINGS
.
242
10.4
EXERCISES
.
244
DETERMINANTAL
IDEALS
.
246
HILBERT
SERIES
OF
A
GRADED
MODULE
.
247
11
DIMENSION
AND
CODIMENSION
ONE
251
11.1
DISCRETE
VALUATION
RINGS
.
251
11.2
NORMAL
RINGS
AND
SERRE
'
S
CRITERION
.
253
11.3
INVERTIBLE
MODULES
.
257
11.4
UNIQUE
FACTORIZATION
OF
CODIMENSION-ONE
IDEALS
.
260
11.5
DIVISORS
AND
MULTIPLICITIES
.
262
11.6
MULTIPLICITY
OF
PRINCIPAL
IDEALS
.
265
11.7
EXERCISES
.
268
VALUATION
RINGS
.
268
THE
GROTHENDIECK
RING
.
269
12
DIMENSION
AND
HILBERT-SAMUEL
POLYNOMIALS
275
12.1
HILBERT-SAMUEL
FUNCTIONS
.
276
12.2
EXERCISES
.
279
ANALYTIC
SPREAD
AND
THE
FIBER
OF
A
BLOWUP
.
280
MULTIPLICITIES
.
280
HILBERT
SERIES
.
284
CONTENTS
XI
13
THE
DIMENSION
OF
AFFINE
RINGS
285
13.1
NOETHER
NORMALIZATION
.
285
13.2
THE
NULLSTELLENSATZ
.
296
13.3
FINITENESS
OF
THE
INTEGRAL
CLOSURE
.
297
13.4
EXERCISES
.
300
QUOTIENTS
BY
FINITE
GROUPS
.
300
PRIMES
IN
POLYNOMIAL
RINGS
.
301
DIMENSION
IN
THE
GRADED
CASE
.
302
NOETHER
NORMALIZATION
IN
THE
COMPLETE
CASE
.
303
PRODUCTS
AND
REDUCTION
TO
THE
DIAGONAL
.
304
EQUATIONAL
CHARACTERIZATION
OF
SYSTEMS
OF
PARAMETERS
306
14
ELIMINATION
THEORY,
GENERIC
FREENESS,
AND
THE
DIMENSION
OF
FIBERS
307
14.1
ELIMINATION
THEORY
.
307
14.2
GENERIC
FREENESS
.
312
14.3
THE
DIMENSION
OF
FIBERS
.
313
14.4
EXERCISES
.
318
ELIMINATION
THEORY
.
318
15
GROBNER
BASES
321
CONSTRUCTIVE
MODULE
THEORY
.
322
ELIMINATION
THEORY
.
322
15.1
MONOMIALS
AND
TERMS
.
323
15.1.1
HILBERT
FUNCTION
AND
POLYNOMIAL
.
324
15.1.2
SYZYGIES
OF
MONOMIAL
SUBMODULES
.
326
15.2
MONOMIAL
ORDERS
.
327
15.3
THE
DIVISION
ALGORITHM
.
333
15.4
GROBNER
BASES
.
335
15.5
SYZYGIES
.
337
15.6
HISTORY
OF
GROBNER
BASES
.
340
15.7
A
PROPERTY
OF
REVERSE
LEXICOGRAPHIC
ORDER
.
342
15.8
GROBNER
BASES
AND
FLAT
FAMILIES
.
345
15.9
GENERIC
INITIAL
IDEALS
.
351
15.9.1
EXISTENCE
OF
THE
GENERIC
INITIAL
IDEAL
.
353
15.9.2
THE
GENERIC
INITIAL
IDEAL
IS
BOREL-FIXED
.
354
15.9.3
THE
NATURE
OF
BOREL-FIXED
IDEALS
.
355
15.10
APPLICATIONS
.
358
15.10.1
IDEAL
MEMBERSHIP
.
359
15.10.2
HILBERT
FUNCTION
AND
POLYNOMIAL
.
359
15.10.3
ASSOCIATED
GRADED
RING
.
360
15.10.4
ELIMINATION
.
361
15.10.5
PROJECTIVE
CLOSURE
AND
IDEAL
AT
INFINITY
.
362
15.10.6
SATURATION
.
363
15.10.7
LIFTING
HOMOMORPHISMS
.
364
XII
CONTENTS
15.10.8
SYZYGIES
AND
CONSTRUCTIVE
MODULE
THEORY
.
365
15.10.9
WHAT
'
S
LEFT?
.
367
15.11
EXERCISES
.
368
15.12
APPENDIX:
SOME
COMPUTER
ALGEBRA
PROJECTS
.
378
PROJECT
1.
ZERO-DIMENSIONAL
GORENSTEIN
IDEALS
.
376
PROJECT
2.
FACTORING
OUT
A
GENERAL
ELEMENT
FROM
AN
STH
SYZYGY
.
377
PROJECT
3.
RESOLUTIONS
OVER
HYPERSURFACES
.
377
PROJECT
4.
RATIONAL
CURVES
OF
DEGREE
R
+
1
IN
P
R
.
.
.
378
PROJECT
5.
REGULARITY
OF
RATIONAL
CURVES
.
378
PROJECT
6.
SOME
MONOMIAL
CURVE
SINGULARITIES
.
379
PROJECT
7.
SOME
INTERESTING
PRIME
IDEALS
.
379
16
MODULES
OF
DIFFERENTIALS
385
16.1
COMPUTATION
OF
DIFFERENTIALS
.
390
16.2
DIFFERENTIALS
AND
THE
COTANGENT
BUNDLE
.
390
16.3
COLIMITS
AND
LOCALIZATION
.
393
16.4
TANGENT
VECTOR
FIELDS
AND
INFINITESIMAL
MORPHISMS
.
398
16.5
DIFFERENTIALS
AND
FIELD
EXTENSIONS
.
400
16.6
JACOBIAN
CRITERION
FOR
REGULARITY
.
404
16.7
SMOOTHNESS
AND
GENERIC
SMOOTHNESS
.
407
16.8
APPENDIX:
ANOTHER
CONSTRUCTION
OF
KAHLER
DIFFERENTIALS
.
410
16.9
EXERCISES
.
412
III
HOMOLOGICAL
METHODS
421
17
REGULAR
SEQUENCES
AND
THE
KOSZUL
COMPLEX
423
17.1
KOSZUL
COMPLEXES
OF
LENGTHS
1
AND
2
.
424
17.2
KOSZUL
COMPLEXES
IN
GENERAL
.
427
17.3
BUILDING
THE
KOSZUL
COMPLEX
FROM
PARTS
.
431
17.4
DUALITY
AND
HOMOTOPIES
.
436
17.5
THE
KOSZUL
COMPLEX
AND
THE
COTANGENT
BUNDLE
OF
PROJECTIVE
SPACE
.
440
17.6
EXERCISES
.
441
FREE
RESOLUTIONS
OF
MONOMIAL
IDEALS
.
443
CONORMAL
SEQUENCE
OF
A
COMPLETE
INTERSECTION
.
444
REGULAR
SEQUENCES
ARE
LIKE
SEQUENCES
OF
VARIABLES
.
445
BLOWUP
ALGEBRA
AND
NORMAL
CONE
OF
A
REGULAR
SEQUENCE
.
445
GEOMETRIC
CONTEXTS
OF
THE
KOSZUL
COMPLEX
.
447
CONTENTS
XIII
18
DEPTH,
CODIMENSION,
AND
COHEN-MACAULAY
RINGS
451
18.1
DEPTH
.
451
18.1.1
DEPTH
AND
THE
VANISHING
OF
EXT
.
453
18.2
COHEN-MACAULAY
RINGS
.
455
18.3
PROVING
PRIMENESS
WITH
SERRE
'
S
CRITERION
.
461
18.4
FLATNESS
AND
DEPTH
.
464
18.5
SOME
EXAMPLES
.
466
18.6
EXERCISES
.
469
19
HOMOLOGICAL
THEORY
OF
REGULAR
LOCAL
RINGS
473
19.1
PROJECTIVE
DIMENSION
AND
MINIMAL
RESOLUTIONS
.
473
19.2
GLOBAL
DIMENSION
AND
THE
SYZYGY
THEOREM
.
478
19.3
DEPTH
AND
PROJECTIVE
DIMENSION:
THE
AUSLANDER
BUCHSBAUM
FORMULA
.
479
19.4
STABLY
FREE
MODULES
AND
FACTORIALITY
OF
REGULAR
LOCAL
RINGS
.
484
19.5
EXERCISES
.
488
REGULAR
RINGS
.
488
MODULES
OVER
A
DEDEKIND
DOMAIN
.
488
THE
AUSLANDER-BUCHSBAUM
FORMULA
.
489
PROJECTIVE
DIMENSION
AND
COHEN-MACAULAY
RINGS
.
.
489
HILBERT
FUNCTION
AND
GROTHENDIECK
GROUP
.
490
THE
CHERN
POLYNOMIAL
.
492
20
FREE
RESOLUTIONS
AND
FITTING
INVARIANTS
493
20.1
THE
UNIQUENESS
OF
FREE
RESOLUTIONS
.
494
20.2
FITTING
IDEALS
.
496
20.3
WHAT
MAKES
A
COMPLEX
EXACT?
.
500
20.4
THE
HILBERT-BURCH
THEOREM
.
506
20.4.1
CUBIC
SURFACES
AND
SEXTUPLES
OF
POINTS
IN
THE
PLANE
.
508
20.5
CASTELNUOVO-MUMFORD
REGULARITY
.
509
20.5.1
REGULARITY
AND
HYPERPLANE
SECTIONS
.
513
20.5.2
REGULARITY
OF
GENERIC
INITIAL
IDEALS
.
514
20.5.3
HISTORICAL
NOTES
ON
REGULARITY
.
514
20.6
EXERCISES
.
515
FITTING
IDEALS
AND
THE
STRUCTURE
OF
MODULES
.
515
PROJECTIVES
OF
CONSTANT
RANK
.
518
CASTELNUOVO-MUMFORD
REGULARITY
.
521
21
DUALITY,
CANONICAL
MODULES,
AND
GORENSTEIN
RINGS
523
21.1
DUALITY
FOR
MODULES
OF
FINITE
LENGTH
.
524
21.2
ZERO-DIMENSIONAL
GORENSTEIN
RINGS
.
529
21.3
CANONICAL
MODULES
AND
GORENSTEIN
RINGS
IN
HIGHER
DIMENSION
.
532
XIV
CONTENTS
21.4
MAXIMAL
COHEN-MACAULAY
MODULES
.
533
21.5
MODULES
OF
FINITE
INJECTIVE
DIMENSION
.
534
21.6
UNIQUENESS
AND
(OFTEN)
EXISTENCE
.
538
21.7
LOCALIZATION
AND
COMPLETION
OF
THE
CANONICAL
MODULE
.
.
540
21.8
COMPLETE
INTERSECTIONS
AND
OTHER
GORENSTEIN
RINGS
.
541
21.9
DUALITY
FOR
MAXIMAL
COHEN-MACAULAY
MODULES
.
542
21.10
LINKAGE
.
543
21.11
DUALITY
IN
THE
GRADED
CASE
.
549
21.12
EXERCISES
.
550
THE
ZERO-DIMENSIONAL
CASE
AND
DUALITY
.
550
HIGHER
DIMENSION
.
552
THE
CANONICAL
MODULE
AS
IDEAL
.
555
LINKAGE
AND
THE
CAYLEY-BACHARACH
THEOREM
.
556
APPENDIX
1
FIELD
THEORY
555
AL.L
TRANSCENDENCE
DEGREE
.
561
AL.
2
SEPARABILITY
.
563
AL.
3
P-BASES
.
565
AL.
3.1
EXERCISES
.
568
APPENDIX
2
MULTILINEAR
ALGEBRA
565
A2.1
INTRODUCTION
.
571
A2.2
TENSOR
PRODUCTS
.
573
A2.3
SYMMETRIC
AND
EXTERIOR
ALGEBRAS
.
574
A2.3.1
BASES
.
578
A2.3.2
EXERCISES
.
580
A2.4
COALGEBRA
STRUCTURES
AND
DIVIDED
POWERS
.
581
A2.4.1
S(M)*
AND
S(AF)
AS
MODULES
OVER
ONE
ANOTHER
.
582
A2.5
SCHUR
FUNCTORS
.
590
A2.5.1
EXERCISES
.
594
A2.6
COMPLEXES
CONSTRUCTED
BY
MULTILINEAR
ALGEBRA
.
596
A2.6.1
STRANDS
OF
THE
KOSZUL
COMPLEX
.
597
A2.6.2
EXERCISES
.
609
APPENDIX
3
HOMOLOGICAL
ALGEBRA
611
A3.1
INTRODUCTION
.
617
PART
I:
RESOLUTIONS
AND
DERIVED
FUNCTORS
.
614
A3.2
FREE
AND
PROJECTIVE
MODULES
.
621
A3.3
FREE
AND
PROJECTIVE
RESOLUTIONS
.
623
A3.4
INJECTIVE
MODULES
AND
RESOLUTIONS
.
624
A3.4.1
EXERCISES
.
630
INJECTIVE
ENVELOPES
.
630
INJECTIVE
MODULES
OVER
NOETHERIAN
RINGS
.
630
A3.5
BASIC
CONSTRUCTIONS
WITH
COMPLEXES
.
632
A3.5.1
NOTATION
AND
DEFINITIONS
.
632
CONTENTS
XV
A3.6
MAPS
AND
HOMOTOPIES
OF
COMPLEXES
.
633
A3.7
EXACT
SEQUENCES
OF
COMPLEXES
.
637
A3.7.1
EXERCISES
.
638
A3.8
THE
LONG
EXACT
SEQUENCE
IN
HOMOLOGY
.
639
A3.8.1
EXERCISES
.
640
DIAGRAMS
AND
SYZYGIES
.
640
A3.9
DERIVED
FUNCTORS
.
643
A3.9.1
EXERCISE
ON
DERIVED
FUNCTORS
.
645
A3.10
TOR
.
646
A3.10.1
EXERCISES:
TOR
.
646
A3.11
EXT
.
649
A3.11.1
EXERCISES:
EXT
.
651
A3.11.2
LOCAL
COHOMOLOGY
.
656
PART
II:
FROM
MAPPING
CONES
TO
SPECTRAL
SEQUENCES
.
.
650
A3.12
THE
MAPPING
CONE
AND
DOUBLE
COMPLEXES
.
656
A3.12.1
EXERCISES:
MAPPING
CONES
AND
DOUBLE
COMPLEXES
660
A3.13
SPECTRAL
SEQUENCES
.
663
A3.13.1
MAPPING
CONES
REVISITED
.
664
A3.13.2
EXACT
COUPLES
.
665
A3.13.3
FILTERED
DIFFERENTIAL
MODULES
AND
COMPLEXES
.
.
.
668
A3.13.4
THE
SPECTRAL
SEQUENCE
OF
A
DOUBLE
COMPLEX
.
.
.
671
A3.13.5
EXACT
SEQUENCE
OF
TERMS
OF
LOW
DEGREE
.
677
A3.13.6
EXERCISES
ON
SPECTRAL
SEQUENCES
.
678
A3.14
DERIVED
CATEGORIES
.
684
A3.14.1
STEP
ONE:
THE
HOMOTOPY
CATEGORY
OF
COMPLEXES
685
A3.14.2
STEP
TWO:
THE
DERIVED
CATEGORY
.
686
A3.14.3
EXERCISES
ON
THE
DERIVED
CATEGORY
.
688
APPENDIX
4
A
SKETCH
OF
LOCAL
COHOMOLOGY
683
A4.1
LOCAL
COHOMOLOGY
AND
GLOBAL
COHOMOLOGY
.
693
A4.2
LOCAL
DUALITY
.
694
A4.3
DEPTH
AND
DIMENSION
.
695
APPENDIX
5
CATEGORY
THEORY
689
A5.1
CATEGORIES,
FUNCTORS,
AND
NATURAL
TRANSFORMATIONS
.
697
A5.2
ADJOINT
FUNCTORS
.
699
A5.2.1
UNIQUENESS
.
700
A5.2.2
SOME
EXAMPLES
.
700
A5.2.3
ANOTHER
CHARACTERIZATION
OF
ADJOINTS
.
701
A5.2.4
ADJOINTS
AND
LIMITS
.
702
A5.3
REPRESENTABLE
FUNCTORS
AND
YONEDA
'
S
LEMMA
.
703
XVI
CONTENTS
APPENDIX
6
LIMITS
AND
COLIMITS
697
A6.1
COLIMITS
IN
THE
CATEGORY
OF
MODULES
.
708
A6.2
FLAT
MODULES
AS
COLIMITS
OF
FREE
MODULES
.
711
A6.3
COLIMITS
IN
THE
CATEGORY
OF
COMMUTATIVE
ALGEBRAS
.
713
A6.4
EXERCISES
.
715
APPENDIX
7
WHERE
NEXT?
709
HINTS
AND
SOLUTIONS
FOR
SELECTED
1
EXERCISES
711
REFERENCES
757
INDEX
OF
NOTATION
775
INDEX
779 |
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| author | Eisenbud, David 1947- |
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| callnumber-raw | QA251.3.E38 1995 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)246385621 (DE-599)BVBBV023597299 |
| dewey-full | 512/.2420 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 20 |
| dewey-search | 512/.24 20 |
| dewey-sort | 3512 224 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. corrected printing |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:42:08Z |
| indexdate | 2024-08-19T00:26:03Z |
| institution | BVB |
| isbn | 3540942696 0387942696 0387942688 |
| language | English |
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| owner_facet | DE-521 |
| physical | XVI, 797 S. 90 graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Eisenbud, David 1947- Verfasser (DE-588)139999671 aut Commutative algebra with view toward algebraic geometry David Eisenbud 3. corrected printing New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo Springer 1999 XVI, 797 S. 90 graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 150 Literaturverz. S. 757 - 774 Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s 1\p DE-604 DE-604 Graduate texts in mathematics 150 (DE-604)BV000000067 150 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912438&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Eisenbud, David 1947- Commutative algebra with view toward algebraic geometry Graduate texts in mathematics Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4001161-6 |
| title | Commutative algebra with view toward algebraic geometry |
| title_auth | Commutative algebra with view toward algebraic geometry |
| title_exact_search | Commutative algebra with view toward algebraic geometry |
| title_exact_search_txtP | Commutative algebra with view toward algebraic geometry |
| title_full | Commutative algebra with view toward algebraic geometry David Eisenbud |
| title_fullStr | Commutative algebra with view toward algebraic geometry David Eisenbud |
| title_full_unstemmed | Commutative algebra with view toward algebraic geometry David Eisenbud |
| title_short | Commutative algebra with view toward algebraic geometry |
| title_sort | commutative algebra with view toward algebraic geometry |
| topic | Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Commutative algebra Geometry, Algebraic Kommutative Algebra Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912438&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT eisenbuddavid commutativealgebrawithviewtowardalgebraicgeometry |