Algebraic geometry: 1 Schemes : with examples and exercises
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Wiesbaden
Vieweg + Teubner
[2020]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Springer Studium Mathematik - Master
|
| Schlagworte: | |
| Online-Zugang: | http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm |
| ISBN: | 9783658307325 3658307323 |
Internformat
MARC
| LEADER | 00000nam a2200000 cc4500 | ||
|---|---|---|---|
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| 003 | DE-604 | ||
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| 007 | t | ||
| 008 | 200904s2020 gw a||| |||| 00||| eng d | ||
| 015 | |a 20,N22 |2 dnb | ||
| 016 | 7 | |a 1210659395 |2 DE-101 | |
| 020 | |a 9783658307325 |c Softcover |9 978-3-658-30732-5 | ||
| 020 | |a 3658307323 |9 3-658-30732-3 | ||
| 035 | |a (OCoLC)1220911098 | ||
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| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Görtz, Ulrich |d 1973- |e Verfasser |0 (DE-588)122267540 |4 aut | |
| 245 | 1 | 0 | |a Algebraic geometry |n 1 |p Schemes : with examples and exercises |c Ulrich Görtz, Torsten Wedhorn |
| 250 | |a Second edition | ||
| 264 | 1 | |a Wiesbaden |b Vieweg + Teubner |c [2020] | |
| 300 | |a VII, 625 Seiten |b 15 Illustrationen |c 24 cm x 16.8 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer Studium Mathematik - Master | |
| 653 | |a morphisms | ||
| 653 | |a vector bundles | ||
| 653 | |a Algebraic Geometry | ||
| 653 | |a algebra | ||
| 653 | |a introduction to schemes | ||
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 700 | 1 | |a Wedhorn, Torsten |d 1970- |e Verfasser |0 (DE-588)120349183 |4 aut | |
| 710 | 2 | |a Springer Fachmedien Wiesbaden |0 (DE-588)1043386068 |4 pbl | |
| 773 | 0 | 8 | |w (DE-604)BV035958399 |g 1 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-658-30733-2 |
| 780 | 0 | 0 | |i Vorangegangen ist |z 978-3-8348-0676-5 |
| 856 | 4 | 2 | |m X:MVB |u http://www.springer.com/ |
| 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=032294219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032294219 | ||
Datensatz im Suchindex
| _version_ | 1804181744063086592 |
|---|---|
| adam_text | CONTENTS
I
NTRODUCTION
1
1
P
REVARIETIES
7
AFFINE
ALGEBRAIC
SETS
................................................................................................
8
AFFINE
ALGEBRAIC
SETS
AS
SPACES
WITH
FUNCTIONS
......................................................
17
PREVARIETIES
...............................................................................................................
23
PROJECTIVE
VARIETIES
...................................................................................................
26
EXERCISES
..................................................................................................................
36
2
S
PECTRUM
OF
A
R
ING
41
SPECTRUM
OF
A
RING
AS
A
TOPOLOGICAL
SPACE
............................................................
42
EXCURSION:
SHEAVES
...................................................................................................
47
SPECTRUM
OF
A
RING
AS
A
LOCALLY
RINGED
SPACE
.........................................................
58
EXERCISES
..................................................................................................................
63
3
S
CHEMES
67
SCHEMES
.....................................................................................................................
67
EXAMPLES
OF
SCHEMES
...............................................................................................
73
BASIC
PROPERTIES
OF
SCHEMES
AND
MORPHISMS
OF
SCHEMES
.....................................
76
PREVARIETIES
AS
SCHEMES
.........................................................................................
80
SUBSCHEMES
AND
IMMERSIONS
...................................................................................
85
EXERCISES
..................................................................................................................
90
4
F
IBER
PRODUCTS
95
SCHEMES
AS
FUNCTORS
...............................................................................................
95
FIBER
PRODUCTS
OF
SCHEMES
......................................................................................
99
BASE
CHANGE,
FIBERS
OF
A
MORPHISM
.....................................................................
107
EXERCISES
..................................................................................................................
117
5
S
CHEMES
OVER
FIELDS
121
SCHEMES
OVER
A
FIELD
WHICH
IS
NOT
ALGEBRAICALLY
CLOSED
........................................
121
DIMENSION
OF
SCHEMES
OVER
A
FIELD
..........................................................................
123
SCHEMES
OVER
FIELDS
AND
EXTENSIONS
OF
THE
BASE
FIELD
...........................................
136
INTERSECTIONS
OF
PLANE
CURVES
...................................................................................
141
EXERCISES
..................................................................................................................
144
6
L
OCAL
P
ROPERTIES
OF
S
CHEMES
148
THE
TANGENT
SPACE
..............................................
149
SMOOTH
MORPHISMS
...........................................................
Z
.....................................
156
REGULAR
SCHEMES
.....................................................................................................
161
NORMAL
SCHEMES
.....................................................................................................
165
EXERCISES
..................................................................................................................
167
VI
CONTENTS
7
Q
UASI
-
COHERENT
MODULES
172
EXCURSION:
^X-MODULES
..........................................................................................
172
QUASI-COHERENT
MODULES
ON
A
SCHEME
....................................................................
184
PROPERTIES
OF
QUASI-COHERENT
MODULES
....................................................................
193
EXERCISES
..................................................................................................................
203
8
R
EPRESENTABLE
F
UNCTORS
208
REPRESENTABLE
FUNCTORS
..........................................................................................
208
THE
EXAMPLE
OF
THE
GRASSMANNIAN
.......................................................................
213
BRAUER-SEVERI
SCHEMES
.............................................................................................
222
EXERCISES
..................................................................................................................
225
9
S
EPARATED
MORPHISMS
230
DIAGONAL
OF
SCHEME
MORPHISMS
AND
SEPARATED
MORPHISMS
...............................
231
RATIONAL
MAPS
AND
FUNCTION
FIELDS
..........................................................................
236
EXERCISES
..................................................................................................................
242
10
F
INITENESS
C
ONDITIONS
244
FINITENESS
CONDITIONS
(NOETHERIAN
CASE)
.................................................................
245
FINITENESS
CONDITIONS
IN
THE
NON-NOETHERIAN
CASE
..............................................
252
SCHEMES
OVER
INDUCTIVE
LIMITS
OF
RINGS
.................................................................
261
CONSTRUCTIBLE
PROPERTIES
..........................................................................................
273
EXERCISES
..................................................................................................................
281
11
V
ECTOR
BUNDLES
288
VECTOR
BUNDLES
AND
LOCALLY
FREE
MODULES
..............................................................
289
FLATTENING
STRATIFICATION
FOR
MODULES
....................................................................
299
DIVISORS
.....................................................................................................................
301
VECTOR
BUNDLES
ON
P
1
................................................................................................
316
EXERCISES
..................................................................................................................
319
12
A
FFINE
AND
PROPER
MORPHISMS
324
AFFINE
MORPHISMS
......................................................................................................
324
FINITE
AND
QUASI-FINITE
MORPHISMS
..........................................................................
328
SERRE
*
S
AND
CHEVALLEY
*
S
CRITERIA
TO
BE
AFFINE
........................................................
338
NORMALIZATION
............................................................................................................
343
PROPER
MORPHISMS
...................................................................................................
347
ZARISKI
*
S
MAIN
THEOREM
.............................................................................................
354
EXERCISES
..................................................................................................................
366
13
P
ROJECTIVE
MORPHISMS
370
PROJECTIVE
SPECTRUM
OF
A
GRADED
ALGEBRA
..............................................................
371
EMBEDDINGS
INTO
PROJECTIVE
SPACE
..........................................................................
389
BLOWING-UP
...............................................................................................................
410
EXERCISES
..................................................................................................................
423
VII
14
F
LAT
MORPHISMS
AND
DIMENSION
428
FLAT
MORPHISMS
.........................................................................................................
428
PROPERTIES
OF
FLAT
MORPHISMS
...................................................................................
436
FAITHFULLY
FLAT
DESCENT
.............................................................................................
446
DIMENSION
AND
FIBERS
OF
MORPHISMS
.......................................................................
470
DIMENSION
AND
REGULARITY
CONDITIONS
....................................................................
479
HILBERT
SCHEMES
.........................................................................................................
484
EXERCISES
..................................................................................................................
487
15
O
NE
-
DIMENSIONAL
SCHEMES
491
MORPHISMS
INTO
AND
FROM
ONE-DIMENSIONAL
SCHEMES
...........................................
491
VALUATIVE
CRITERIA
......................................................................................................
493
CURVES
OVER
FIELDS
......................................................................................................
497
DIVISORS
ON
CURVES
...................................................................................................
501
EXERCISES
..................................................................................................................
506
16
E
XAMPLES
508
DETERMINANTAL
VARIETIES
.........................................................................................
508
CUBIC
SURFACES
AND
A
HILBERT
MODULAR
SURFACE
......................................................
525
CYCLIC
QUOTIENT
SINGULARITIES
...................................................................................
534
ABELIAN
VARIETIES
......................................................................................................
538
EXERCISES
..................................................................................................................
545
A
T
HE
LANGUAGE
OF
CATEGORIES
547
B
C
OMMUTATIVE
A
LGEBRA
554
C
P
ERMANENCE
FOR
PROPERTIES
OF
MORPHISMS
OF
SCHEMES
582
D
R
ELATIONS
BETWEEN
PROPERTIES
OF
MORPHISMS
OF
SCHEMES
585
E
CONSTRUCTIBLE
AND
OPEN
PROPERTIES
587
B
IBLIOGRAPHY
592
D
ETAILED
L
IST
OF
C
ONTENTS
597
I
NDEX
OF
S
YMBOLS
607
I
NDEX
611
|
| adam_txt |
CONTENTS
I
NTRODUCTION
1
1
P
REVARIETIES
7
AFFINE
ALGEBRAIC
SETS
.
8
AFFINE
ALGEBRAIC
SETS
AS
SPACES
WITH
FUNCTIONS
.
17
PREVARIETIES
.
23
PROJECTIVE
VARIETIES
.
26
EXERCISES
.
36
2
S
PECTRUM
OF
A
R
ING
41
SPECTRUM
OF
A
RING
AS
A
TOPOLOGICAL
SPACE
.
42
EXCURSION:
SHEAVES
.
47
SPECTRUM
OF
A
RING
AS
A
LOCALLY
RINGED
SPACE
.
58
EXERCISES
.
63
3
S
CHEMES
67
SCHEMES
.
67
EXAMPLES
OF
SCHEMES
.
73
BASIC
PROPERTIES
OF
SCHEMES
AND
MORPHISMS
OF
SCHEMES
.
76
PREVARIETIES
AS
SCHEMES
.
80
SUBSCHEMES
AND
IMMERSIONS
.
85
EXERCISES
.
90
4
F
IBER
PRODUCTS
95
SCHEMES
AS
FUNCTORS
.
95
FIBER
PRODUCTS
OF
SCHEMES
.
99
BASE
CHANGE,
FIBERS
OF
A
MORPHISM
.
107
EXERCISES
.
117
5
S
CHEMES
OVER
FIELDS
121
SCHEMES
OVER
A
FIELD
WHICH
IS
NOT
ALGEBRAICALLY
CLOSED
.
121
DIMENSION
OF
SCHEMES
OVER
A
FIELD
.
123
SCHEMES
OVER
FIELDS
AND
EXTENSIONS
OF
THE
BASE
FIELD
.
136
INTERSECTIONS
OF
PLANE
CURVES
.
141
EXERCISES
.
144
6
L
OCAL
P
ROPERTIES
OF
S
CHEMES
148
THE
TANGENT
SPACE
.
149
SMOOTH
MORPHISMS
.
Z
.
156
REGULAR
SCHEMES
.
161
NORMAL
SCHEMES
.
165
EXERCISES
.
167
VI
CONTENTS
7
Q
UASI
-
COHERENT
MODULES
172
EXCURSION:
^X-MODULES
.
172
QUASI-COHERENT
MODULES
ON
A
SCHEME
.
184
PROPERTIES
OF
QUASI-COHERENT
MODULES
.
193
EXERCISES
.
203
8
R
EPRESENTABLE
F
UNCTORS
208
REPRESENTABLE
FUNCTORS
.
208
THE
EXAMPLE
OF
THE
GRASSMANNIAN
.
213
BRAUER-SEVERI
SCHEMES
.
222
EXERCISES
.
225
9
S
EPARATED
MORPHISMS
230
DIAGONAL
OF
SCHEME
MORPHISMS
AND
SEPARATED
MORPHISMS
.
231
RATIONAL
MAPS
AND
FUNCTION
FIELDS
.
236
EXERCISES
.
242
10
F
INITENESS
C
ONDITIONS
244
FINITENESS
CONDITIONS
(NOETHERIAN
CASE)
.
245
FINITENESS
CONDITIONS
IN
THE
NON-NOETHERIAN
CASE
.
252
SCHEMES
OVER
INDUCTIVE
LIMITS
OF
RINGS
.
261
CONSTRUCTIBLE
PROPERTIES
.
273
EXERCISES
.
281
11
V
ECTOR
BUNDLES
288
VECTOR
BUNDLES
AND
LOCALLY
FREE
MODULES
.
289
FLATTENING
STRATIFICATION
FOR
MODULES
.
299
DIVISORS
.
301
VECTOR
BUNDLES
ON
P
1
.
316
EXERCISES
.
319
12
A
FFINE
AND
PROPER
MORPHISMS
324
AFFINE
MORPHISMS
.
324
FINITE
AND
QUASI-FINITE
MORPHISMS
.
328
SERRE
*
S
AND
CHEVALLEY
*
S
CRITERIA
TO
BE
AFFINE
.
338
NORMALIZATION
.
343
PROPER
MORPHISMS
.
347
ZARISKI
*
S
MAIN
THEOREM
.
354
EXERCISES
.
366
13
P
ROJECTIVE
MORPHISMS
370
PROJECTIVE
SPECTRUM
OF
A
GRADED
ALGEBRA
.
371
EMBEDDINGS
INTO
PROJECTIVE
SPACE
.
389
BLOWING-UP
.
410
EXERCISES
.
423
VII
14
F
LAT
MORPHISMS
AND
DIMENSION
428
FLAT
MORPHISMS
.
428
PROPERTIES
OF
FLAT
MORPHISMS
.
436
FAITHFULLY
FLAT
DESCENT
.
446
DIMENSION
AND
FIBERS
OF
MORPHISMS
.
470
DIMENSION
AND
REGULARITY
CONDITIONS
.
479
HILBERT
SCHEMES
.
484
EXERCISES
.
487
15
O
NE
-
DIMENSIONAL
SCHEMES
491
MORPHISMS
INTO
AND
FROM
ONE-DIMENSIONAL
SCHEMES
.
491
VALUATIVE
CRITERIA
.
493
CURVES
OVER
FIELDS
.
497
DIVISORS
ON
CURVES
.
501
EXERCISES
.
506
16
E
XAMPLES
508
DETERMINANTAL
VARIETIES
.
508
CUBIC
SURFACES
AND
A
HILBERT
MODULAR
SURFACE
.
525
CYCLIC
QUOTIENT
SINGULARITIES
.
534
ABELIAN
VARIETIES
.
538
EXERCISES
.
545
A
T
HE
LANGUAGE
OF
CATEGORIES
547
B
C
OMMUTATIVE
A
LGEBRA
554
C
P
ERMANENCE
FOR
PROPERTIES
OF
MORPHISMS
OF
SCHEMES
582
D
R
ELATIONS
BETWEEN
PROPERTIES
OF
MORPHISMS
OF
SCHEMES
585
E
CONSTRUCTIBLE
AND
OPEN
PROPERTIES
587
B
IBLIOGRAPHY
592
D
ETAILED
L
IST
OF
C
ONTENTS
597
I
NDEX
OF
S
YMBOLS
607
I
NDEX
611 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Görtz, Ulrich 1973- Wedhorn, Torsten 1970- |
| author_GND | (DE-588)122267540 (DE-588)120349183 |
| author_facet | Görtz, Ulrich 1973- Wedhorn, Torsten 1970- |
| author_role | aut aut |
| author_sort | Görtz, Ulrich 1973- |
| author_variant | u g ug t w tw |
| building | Verbundindex |
| bvnumber | BV046884276 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)1220911098 (DE-599)DNB1210659395 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV046884276 |
| illustrated | Illustrated |
| index_date | 2024-07-03T15:19:06Z |
| indexdate | 2024-07-10T08:56:31Z |
| institution | BVB |
| institution_GND | (DE-588)1043386068 |
| isbn | 9783658307325 3658307323 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032294219 |
| oclc_num | 1220911098 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-11 |
| physical | VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Vieweg + Teubner |
| record_format | marc |
| series2 | Springer Studium Mathematik - Master |
| spelling | Görtz, Ulrich 1973- Verfasser (DE-588)122267540 aut Algebraic geometry 1 Schemes : with examples and exercises Ulrich Görtz, Torsten Wedhorn Second edition Wiesbaden Vieweg + Teubner [2020] VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm txt rdacontent n rdamedia nc rdacarrier Springer Studium Mathematik - Master morphisms vector bundles Algebraic Geometry algebra introduction to schemes (DE-588)4123623-3 Lehrbuch gnd-content Wedhorn, Torsten 1970- Verfasser (DE-588)120349183 aut Springer Fachmedien Wiesbaden (DE-588)1043386068 pbl (DE-604)BV035958399 1 Erscheint auch als Online-Ausgabe 978-3-658-30733-2 Vorangegangen ist 978-3-8348-0676-5 X:MVB http://www.springer.com/ DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Görtz, Ulrich 1973- Wedhorn, Torsten 1970- Algebraic geometry |
| subject_GND | (DE-588)4123623-3 |
| title | Algebraic geometry |
| title_auth | Algebraic geometry |
| title_exact_search | Algebraic geometry |
| title_exact_search_txtP | Algebraic geometry |
| title_full | Algebraic geometry 1 Schemes : with examples and exercises Ulrich Görtz, Torsten Wedhorn |
| title_fullStr | Algebraic geometry 1 Schemes : with examples and exercises Ulrich Görtz, Torsten Wedhorn |
| title_full_unstemmed | Algebraic geometry 1 Schemes : with examples and exercises Ulrich Görtz, Torsten Wedhorn |
| title_short | Algebraic geometry |
| title_sort | algebraic geometry schemes with examples and exercises |
| topic_facet | Lehrbuch |
| url | http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035958399 |
| work_keys_str_mv | AT gortzulrich algebraicgeometry1 AT wedhorntorsten algebraicgeometry1 AT springerfachmedienwiesbaden algebraicgeometry1 |