The algebraic and geometric theory of quadratic forms
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2008
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| Schriftenreihe: | American Mathematical Society Colloquium publications
volume 56 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 020 | |a 9780821843291 |9 978-0-8218-4329-1 | ||
| 035 | |a (OCoLC)185095764 | ||
| 035 | |a (DE-599)BVBBV023304260 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
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| 100 | 1 | |a Elman, Richard S. |d 1945- |e Verfasser |0 (DE-588)172714710 |4 aut | |
| 245 | 1 | 0 | |a The algebraic and geometric theory of quadratic forms |c Richard Elman ; Nikita Karpenko ; Alexander Merkurjev |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2008 | |
| 264 | 4 | |c © 2008 | |
| 300 | |a VIII, 435 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society Colloquium publications |v volume 56 | |
| 650 | 4 | |a Bilinear forms | |
| 650 | 4 | |a Forms, Quadratic | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quadratische Form |0 (DE-588)4128297-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quadratische Form |0 (DE-588)4128297-8 |D s |
| 689 | 0 | 1 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Karpenko, Nikita |d 1966- |e Verfasser |0 (DE-588)1224976835 |4 aut | |
| 700 | 1 | |a Merkurev, Aleksandr S. |d 1955- |e Verfasser |0 (DE-588)1088596533 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-3202-7 |
| 830 | 0 | |a American Mathematical Society Colloquium publications |v volume 56 |w (DE-604)BV035417609 |9 56 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016488659 | |
Datensatz im Suchindex
| _version_ | 1819635172047323136 |
|---|---|
| adam_text | Contents
Introduction
Part
1.
Classical theory of symmetric bilinear forms and quadratic
forms
9
Chapter I. Bilinear Forms
11
1.
Foundations
H
2.
The Witt and Witt-Grothendieck rings of symmetric bilinear forms
19
3.
Chain equivalence
21
4.
Structure of the Witt ring
22
5.
The
Stiefel-
Whitney map
28
6.
Bilinear Pfister forms
32
Chapter II. Quadratic Forms
39
7.
Foundations
39
8.
Witt s Theorems
46
9.
Quadratic Pfister forms I
52
10.
Totally singular forms
55
11.
The Clifford algebra
57
12.
Binary quadratic forms and quadratic algebras
60
13.
The discriminant
61
14.
The Clifford invariant
63
15.
Chain p-equivalence of quadratic Pfister forms
64
16.
Cohomological invariants
67
Chapter III. Forms over Rational Function Fields
71
17.
The Cassels-Pfister Theorem
71
18.
Values of forms
75
19.
Forms over a discrete valuation ring
79
20.
Similarities of forms
82
21.
An exact sequence for W{F{t))
88
Chapter IV. Function Fields of Quadrics
93
22.
Quadrics
93
23.
Quadratic Pfister forms II
98
24.
Linkage of quadratic forms
101
25.
The
submodule Jn(F)
103
26.
The Separation Theorem
107
27.
A further characterization of quadratic Pfister forms
109
28.
Excellent quadratic forms
Ш
vi
CONTENTS
29.
Excellent field extensions
113
30.
Central simple algebras over function fields of quadratic forms
116
Chapter V. Bilinear and Quadratic Forms and Algebraic Extensions
121
31.
Structure of the Witt ring
121
32.
Addendum on torsion
131
33.
The total signature
133
34.
Bilinear and quadratic forms under quadratic extensions
138
35.
Torsion in In(F) and torsion Pfister forms
147
Chapter VI. u-invariants
161
36.
The u-invariant
161
37.
The u-invariant for formally real fields
165
38.
Construction of fields with even u-invariant
170
39.
Addendum: Linked fields and the
Hasse
number
172
Chapter
VII.
Applications of the Milnor Conjecture
177
40.
Exact sequences for quadratic extensions
177
41.
Annihilators of Pfister forms
181
42.
Presentation of In(F)
184
43.
Going down and torsion-freeness
188
Chapter
VIII.
On the Norm Residue Homomorphism of Degree Two
193
44.
The main theorem
193
45.
Geometry of conic curves
194
46.
Key exact sequence
198
47.
Hubert Theorem
90
for K2
208
48.
Proof of the main theorem
211
Part
2.
Algebraic cycles
215
Chapter IX. Homology and Cohomology
217
49.
The complex
C*(X)
217
50.
External products
232
51.
Deformation homomorphisms
235
52.
if-homology groups
238
53.
Euler
classes and
projective
bundle theorem
243
54.
Chern classes
247
55.
Gysin and pull-back homomorphisms
250
56.
if-cohomology ring of smooth schemes
257
Chapter X. Chow Groups
261
57.
Definition of Chow groups
261
58.
Segre
and Chern classes
268
Chapter XL Steenrod Operations
277
59.
Definition of the Steenrod operations
278
60.
Properties of the Steenrod operations
281
61.
Steenrod operations for smooth schemes
283
Chapter
XII.
Category of Chow Motives
291
CONTENTS
vii
62. Correspondences 291
63.
Categories of correspondences
295
64.
Category of Chow motives
298
65.
Duality
299
66.
Motives of cellular schemes
300
67.
Nilpotence Theorem
302
Part
3.
Quadratic forms and algebraic cycles
305
Chapter
XIII.
Cycles on Powers of Quadrics
307
68.
Split quadrics
307
69.
Isomorphisms of quadrics
309
70. Isotropie
quadrics
310
71.
The Chow group of dimension
0
cycles on quadrics
311
72.
The reduced Chow group
313
73.
Cycles on X2
316
Chapter
XIV.
The Izhboldin Dimension
325
74.
The first Witt index of subforms
325
75.
Correspondences
326
76.
The main theorem
329
77.
Addendum: The Pythagoras number
332
Chapter XV. Application of Steenrod Operations
335
78.
Computation of Steenrod operations
335
79.
Values of the first Witt index
336
80. Rost
correspondences
339
81.
On the 2-adic order of higher Witt indices, I
342
82.
Holes in
Γ
347
83.
On the 2-adic order of higher Witt indices, II
350
84.
Minimal height
351
Chapter
XVI.
The Variety of Maximal Totally
Isotropie
Subspaees
355
85.
The variety Gr(^)
355
86.
The Chow ring of Gr(y) in the split case
356
87.
The Chow ring of Gr(<^) in the general case
361
88.
The invariant
J
(φ)
364
89.
Steenrod operations on
Ch(Gr(<¿>))
366
90.
Canonical dimension
367
Chapter
XVII.
Motives of Quadrics
371
91.
Comparison of some discrete invariants of quadratic forms
371
92.
The Nilpotence Theorem for quadrics
373
93.
Criterion of isomorphism
375
94.
Indecomposable summands
378
Appendices
381
95.
Formally real fields
383
96.
The space of orderings
384
97.
CW-fields
385
viii CONTENTS
98.
Algebras
387
99.
Galois cohomology
393
100.
Milnor K-theory of fields
397
101.
The cohomology groups Hn^{F,
Ћ/тЋ)
402
102.
Length and
Herbrand
index
407
103.
Places
408
104.
Cones and vector bundles
409
105.
Group actions on algebraic schemes
418
Bibliography
421
Notation
427
Terminology
431
|
| any_adam_object | 1 |
| author | Elman, Richard S. 1945- Karpenko, Nikita 1966- Merkurev, Aleksandr S. 1955- |
| author_GND | (DE-588)172714710 (DE-588)1224976835 (DE-588)1088596533 |
| author_facet | Elman, Richard S. 1945- Karpenko, Nikita 1966- Merkurev, Aleksandr S. 1955- |
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| ctrlnum | (OCoLC)185095764 (DE-599)BVBBV023304260 |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV023304260 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T21:00:34Z |
| institution | BVB |
| isbn | 9780821843291 |
| language | English |
| lccn | 2007060599 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016488659 |
| oclc_num | 185095764 |
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| physical | VIII, 435 Seiten |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | American Mathematical Society Colloquium publications |
| series2 | American Mathematical Society Colloquium publications |
| spellingShingle | Elman, Richard S. 1945- Karpenko, Nikita 1966- Merkurev, Aleksandr S. 1955- The algebraic and geometric theory of quadratic forms American Mathematical Society Colloquium publications Bilinear forms Forms, Quadratic Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Quadratische Form (DE-588)4128297-8 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4128297-8 |
| title | The algebraic and geometric theory of quadratic forms |
| title_auth | The algebraic and geometric theory of quadratic forms |
| title_exact_search | The algebraic and geometric theory of quadratic forms |
| title_full | The algebraic and geometric theory of quadratic forms Richard Elman ; Nikita Karpenko ; Alexander Merkurjev |
| title_fullStr | The algebraic and geometric theory of quadratic forms Richard Elman ; Nikita Karpenko ; Alexander Merkurjev |
| title_full_unstemmed | The algebraic and geometric theory of quadratic forms Richard Elman ; Nikita Karpenko ; Alexander Merkurjev |
| title_short | The algebraic and geometric theory of quadratic forms |
| title_sort | the algebraic and geometric theory of quadratic forms |
| topic | Bilinear forms Forms, Quadratic Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Quadratische Form (DE-588)4128297-8 gnd |
| topic_facet | Bilinear forms Forms, Quadratic Geometry, Algebraic Algebraische Geometrie Quadratische Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417609 |
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