Algebraic geometry: 1 Schemes : with examples and exercises
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Wiesbaden
Vieweg + Teubner
[2020]
Wiesbaden 2010- |
| Edition: | Second edition |
| Series: | Springer Studium Mathematik - Master |
| Subjects: | |
| Online Access: | http://www.springer.com/ Inhaltsverzeichnis |
| Physical Description: | VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm |
| ISBN: | 9783658307325 3658307323 |
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MARC
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| 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 | |c [2020] | |
| 264 | 1 | |a Wiesbaden |b Vieweg + Teubner | |
| 264 | 4 | |c © 2020 | |
| 264 | 1 | |a Wiesbaden |b Vieweg + Teubner |c 2010- | |
| 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 | ||
| 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 | |
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Record in the Search Index
| _version_ | 1829651076196859904 |
|---|---|
| adam_text | |
| 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 |
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| author | Görtz, Ulrich 1973- Wedhorn, Torsten 1970- |
| author_GND | (DE-588)122267540 (DE-588)120349183 |
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| 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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| illustrated | Illustrated |
| index_date | 2024-07-03T15:19:06Z |
| indexdate | 2025-04-17T12:00:39Z |
| institution | BVB |
| institution_GND | (DE-588)1043386068 |
| isbn | 9783658307325 3658307323 |
| language | English German |
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| physical | VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm |
| publishDate | 2020 2010 |
| 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 [2020] Wiesbaden Vieweg + Teubner © 2020 Wiesbaden Vieweg + Teubner 2010- VII, 625 Seiten 15 Illustrationen 24 cm x 16.8 cm txt rdacontent n rdamedia nc rdacarrier 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 https://bvbr.bib-bvb.de:443/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/ https://bvbr.bib-bvb.de:443/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 |