Cubic forms: algebra, geometry, arithmetic
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Amsterdam u.a.
North-Holland
1986
|
| Edition: | 2. ed. |
| Series: | North-Holland mathematical library
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 326 S. |
| ISBN: | 0444878238 |
Staff View
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Record in the Search Index
| _version_ | 1804114989817004032 |
|---|---|
| adam_text | CONTENTS
PREFACE TO THE SECOND EDITION v
CONTENTS vii
INSTRUCTIONS TO THE READER x
INTRODUCTION 1
CHAPTER I. CH QUASIGROUPS AND MOUFANG LOOPS 6
1. A survey of definitions and results 6
2. Symmetric Abelian quasigroups 11
3. CH quasigroups 15
4. Commutative Moufang loops 21
5. The connection between CH quasigroups and Moufang loops ... 25
6. Morphisms of CH quasigroups and Moufang loops 28
7. The first structure theorem 30
8. The second structure theorem 33
9. Finite Fischer groups 34
10. Unsolved problems and bibliographical remarks 39
CHAPTER II. CLASSES OF POINTS ON CUBIC HYPERSURFACES 42
11. Admissible equivalence relations: a survey 42
12. Unirationality 46
13. Universal equivalence 54
14. R equivalence: the basic properties 61
15. R equivalence and quadratic extensions 65
16. Universal equivalence over local fields. Examples 69
17. Bibliographical remarks 76
CHAPTER III. TWO DIMENSIONAL BIRATIONAL GEOMETRY 77
18. The main results 77
19. Monoidal transformations 82
20. Monoidal transformations and divisors 90
21. The main theorems on birational maps 100
22. Bibliographical remarks 110
vii
vi» CONTENTS
CHAPTER IV. THE TWENTY SEVEN LINES 112
23. A survey of the results 112
24. Del Pezzo surfaces 117
25. The Picard group and root systems 126
26. Exceptional curves and Weyl groups 134
27. The zeta function 143
28. Minimality and classes of conjugate elements in Weyl groups . ¦ .151
29. A cohomological invariant and the degree of unirationality. . . .154
30. Rational points 162
31. Tables and comments. Calculation of//1. The theorem of Artin
andTate 174
32. Bibliographical remarks 182
CHAPTER V. MINIMAL CUBIC SURFACES 184
33. A survey of the results 184
34. The fundamental birational invariant 189
35. /. bubble space 195
36. Calculations on cubic surfaces 200
37. Birational non triviality 202
38. Birational classification 204
39. Relations between the generators 206
40. Bibliographical remarks 219
CHAPTER VI. THE BRAUER GROTHENDIECK GROUP 220
41. A survey of the results. Obstructions to the Hasse principle .... 220
42. The construction of Azumaya algebras 229
43. Brauer equivalence 234
44. The finiteness theorem 237
45. Calculations for Brauer equivalence. Examples 243
46. A negative result 264
47. Counter examples to the Hasse principle 276
48. Bibliographical remarks 283
APPENDIX. ALGEBRAIC VARIETIES CLOSE TO THE RATIONAL ONES.
ALGEBRA, GEOMETRY, ARITHMETIC
Introduction 284
1. Galois cohomology, Picard groups and birational geometry .... 285
2. The Hasse principle and descent on rational varieties 288
3. Geometry of rational surfaces. Complements 294
CONTENTS ix
4. The Liiroth problem and the Zariski problem in dimension s* 3 ... 302
5. Rational points and equivalence relations 306
6. Cubic surfaces and commutative Moufang loops (CML) 309
References (for the Appendix) 313
REFERENCES 318
AUTHOR INDEX 323
LIST OF SYMBOLS 324
SUBJECT INDEX 325
|
| any_adam_object | 1 |
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| author_facet | Manin, Jurij I. 1937-2023 |
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| building | Verbundindex |
| bvnumber | BV000545103 |
| classification_rvk | SK 180 |
| classification_tum | MAT 103f |
| ctrlnum | (OCoLC)246747504 (DE-599)BVBBV000545103 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV000545103 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:15:29Z |
| institution | BVB |
| isbn | 0444878238 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000336017 |
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| physical | X, 326 S. |
| psigel | TUB-www |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Manin, Jurij I. 1937-2023 Verfasser (DE-588)121177580 aut Kubičeskie formy Cubic forms algebra, geometry, arithmetic Yu. I. Manin 2. ed. Amsterdam u.a. North-Holland 1986 X, 326 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 4 Aus dem Russ. übers. Brauer-Gruppe - Kubische Hyperfläche Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kubische Form (DE-588)4569782-6 gnd rswk-swf Kubische Form (DE-588)4569782-6 s DE-604 Zahlentheorie (DE-588)4067277-3 s North-Holland mathematical library 4 (DE-604)BV000005206 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000336017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manin, Jurij I. 1937-2023 Cubic forms algebra, geometry, arithmetic North-Holland mathematical library Brauer-Gruppe - Kubische Hyperfläche Zahlentheorie (DE-588)4067277-3 gnd Kubische Form (DE-588)4569782-6 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4569782-6 |
| title | Cubic forms algebra, geometry, arithmetic |
| title_alt | Kubičeskie formy |
| title_auth | Cubic forms algebra, geometry, arithmetic |
| title_exact_search | Cubic forms algebra, geometry, arithmetic |
| title_full | Cubic forms algebra, geometry, arithmetic Yu. I. Manin |
| title_fullStr | Cubic forms algebra, geometry, arithmetic Yu. I. Manin |
| title_full_unstemmed | Cubic forms algebra, geometry, arithmetic Yu. I. Manin |
| title_short | Cubic forms |
| title_sort | cubic forms algebra geometry arithmetic |
| title_sub | algebra, geometry, arithmetic |
| topic | Brauer-Gruppe - Kubische Hyperfläche Zahlentheorie (DE-588)4067277-3 gnd Kubische Form (DE-588)4569782-6 gnd |
| topic_facet | Brauer-Gruppe - Kubische Hyperfläche Zahlentheorie Kubische Form |
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