Algebraic geometry: 1 Schemes : with examples and exercises
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg + Teubner
2010
|
| Ausgabe: | 1st edition |
| Schriftenreihe: | Advanced lectures in mathematics
Springer Studium Mathematik - Master |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 615 Seiten Diagramme |
| ISBN: | 9783834806765 |
Internformat
MARC
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| 020 | |a 9783834806765 |c softcover |9 978-3-8348-0676-5 | ||
| 035 | |a (OCoLC)633125097 | ||
| 035 | |a (DE-599)BVBBV035958410 | ||
| 040 | |a DE-604 |b ger |e rda | ||
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| 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 1st edition | ||
| 264 | 1 | |a Wiesbaden |b Vieweg + Teubner |c 2010 | |
| 300 | |a vii, 615 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Advanced lectures in mathematics | |
| 490 | 0 | |a Springer Studium Mathematik - Master | |
| 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 | |
| 773 | 0 | 8 | |w (DE-604)BV035958399 |g 1 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-8348-9722-0 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018852622 | ||
Datensatz im Suchindex
| _version_ | 1804140975093710848 |
|---|---|
| adam_text | v
Contents
Introduction
1
1
Prevarieties
7
Affine
algebraic sets
................................ 8
Affine
algebraic sets as spaces with functions
.................. 17
Prevarieties
..................................... 22
Projective
varieties
................................. 26
Exercises
...................................... 35
2
Spectrum of a Ring
40
Spectrum of a ring as a topological space
.................... 41
Excursion: Sheaves
................................. 46
Spectrum of a ring as a locally ringed space
................... 57
Exercises
...................................... 62
3
Schemes
66
Schemes
....................................... 66
Examples of schemes
................................ 72
Basic properties of schemes and morphisms of schemes
............. 74
Prevarieties as Schemes
.............................. 78
Subschemes and Immersions
............................ 83
Exercises
...................................... 88
4
Fiber products
93
Schemes as functors
................................ 93
Fiber products of schemes
............................. 97
Base change, Fibers of a morphism
........................ 105
Exercises
...................................... 114
5
Schemes over fields
118
Schemes over a field which is not algebraically closed
.............. 118
Dimension of schemes over a field
......................... 120
Schemes over fields and extensions of the base field
............... 133
Intersections of plane curves
............................ 138
Exercises
...................................... 141
6
Local Properties of Schemes
145
The tangent space
................................. 146
Smooth morphisms
................................. 153
Regular schemes
.................................. 158
Normal schemes
.................................. 161
Exercises
...................................... 164
VI
Contents
7
Quasi-coherent modules
169
Excursion:
^χ
-modules
.............................. 169
Quasi-coherent modules on a scheme
....................... 181
Properties of quasi-coherent modules
....................... 189
Exercises
...................................... 199
8
Representadle
Functors
205
Representable Functors
.............................. 206
The example of the Grassmannian
........................ 209
Brauer-Severi schemes
............................... 219
Exercises
...................................... 222
9
Separated morphisms
226
Diagonal of scheme morphisms and separated morphisms
........... 226
Rational maps and function fields
......................... 232
Exercises
...................................... 238
10
Finiteness Conditions
241
Finiteness conditions (noetherian case)
...................... 242
Finiteness conditions in the non-noetherian case
................ 249
Schemes over inductive limits of rings
...................... 258
Constructible
properties
.............................. 270
Exercises
...................................... 278
11
Vector bundles
286
Vector bundles and locally free modules
..................... 286
Flattening stratification for modules
....................... 296
Divisors
....................................... 298
Vector bundles on P1
................................ 313
Exercises
...................................... 316
12
Affine
and proper morphisms
320
Affine
morphisms
.................................. 320
Finite and quasi-finite morphisms
......................... 324
Serre s and Chevalley s criteria to be
affine
................... 334
Normalization
.................................... 339
Proper morphisms
................................. 343
Zariski s main theorem
............................... 349
Exercises
...................................... 361
13
Projectíve morphisms
366
Projective
spectrum of a graded algebra
..................... 367
Embeddings into
projective
space
......................... 384
Blowing-up
..................................... 406
Exercises
...................................... 418
__________________________________________________________________
VII
14
Flat morphisms and dimension
423
Flat morphisms
................................... 423
Properties of flat morphisms
............................ 429
Faithfully flat descent
............................... 439
Dimension and fibers of morphisms
........................ 463
Dimension and regularity conditions
....................... 473
Hubert schemes
................................... 478
Exercises
...................................... 480
15
One-dimensional schemes
485
Morphisms into and from one-dimensional schemes
............... 485
Valuative criteria
.................................. 487
Curves over fields
.................................. 491
Divisors on curves
................................. 496
Exercises
...................................... 500
16
Examples
503
Determinantal varieties
.............................. 503
Cubic surfaces and a Hubert modular surface
.................. 520
Cyclic quotient singularities
............................ 528
Abelian varieties
.................................. 532
Exercises
...................................... 539
A The language of categories
541
В
Commutative Algebra
547
С
Permanence for properties of morphisms of schemes
573
D
Relations between properties of morphisms of schemes
576
E
Constructible
and open properties
578
Bibliography
583
Detailed List of Contents
588
Index of Symbols
598
Index
602
|
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| genre_facet | Lehrbuch |
| id | DE-604.BV035958410 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:08:31Z |
| institution | BVB |
| isbn | 9783834806765 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018852622 |
| oclc_num | 633125097 |
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| physical | vii, 615 Seiten Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Vieweg + Teubner |
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| series2 | Advanced lectures in mathematics 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 1st edition Wiesbaden Vieweg + Teubner 2010 vii, 615 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Advanced lectures in mathematics Springer Studium Mathematik - Master (DE-588)4123623-3 Lehrbuch gnd-content Wedhorn, Torsten 1970- Verfasser (DE-588)120349183 aut (DE-604)BV035958399 1 Erscheint auch als Online-Ausgabe 978-3-8348-9722-0 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018852622&sequence=000002&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_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://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018852622&sequence=000002&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 |