The K-book: an introduction to algebraic K-theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2013
|
| Series: | Graduate studies in mathematics
145 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 618 S. graph. Darst. |
| ISBN: | 9780821891322 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804150300831907840 |
|---|---|
| adam_text | Titel: The K-book
Autor: Weibel, Charles A
Jahr: 2013
Contents
Preface ix
Acknowledgements xii
Chapter I. Projective modules and vector bundles 1
§1. Free modules, GLn, and stably free modules 1
§2. Projective modules 8
§3. The Picard group of a commutative ring 20
§4. Topological vector bundles and Chern classes 34
§5. Algebraic vector bundles 49
Chapter II. The Grothendieck group Ko 69
§1. The group completion of a monoid 69
§2. Ko of a ring 74
§3. K(X), KO(X), and KU(X) of a topological space 89
§4. Lambda and Adams operations 98
§5. Ko of a symmetric monoidal category 114
§6. K0 of an abelian category 124
§7. Ko of an exact category 140
§8. K0 of schemes and varieties 157
§9. K0 of a Waldhausen category 172
Appendix. Localizing by calculus of fractions 189
Chapter III. K and K2 of a ring 197
§1. The Whitehead group Ki of a ring 197
V
vi
Contents
§2. Relative ifi 212
§3. The Fundamental Theorems for K and ifo 217
§4. Negative if-theory 229
§5. K2 of a ring 236
§6. if2 of fields 251
§7. Milnor if-theory of fields 266
Chapter IV. Definitions of higher if-theory 283
§1. The BGL+ definition for rings 284
§2. if-theory with finite coefficients 304
§3. Geometric realization of a small category 311
§4. Symmetric monoidal categories 326
§5. A-operations in higher if-theory 341
§6. Quillen s Q-construction for exact categories 347
§7. The + = Q Theorem 358
§8. Waldhausen s wS. construction 364
§9. The Gillet-Grayson construction 377
§10. Nonconnective spectra in if-theory 381
§11. Karoubi-Villamayor if-theory 385
§12. Homotopy if-theory 394
Chapter V. The Fundamental Theorems of higher if-theory 401
§1. The Additivity Theorem 401
§2. Waldhausen localization and approximation 413
§3. The Resolution Theorems and transfer maps 423
§4. Devissage 439
§5. The Localization Theorem for abelian categories 442
§6. Applications of the Localization Theorem 445
§7. Localization for if*(i2) and K*(X) 462
§8. The Fundamental Theorem for K„(R) and K*(X) 472
§9. The coniveau spectral sequence of Gersten and Quillen 477
§10. Descent and Mayer-Vietoris properties 486
§11. Chern classes 494
Chapter VI. The higher if-theory of fields 509
§1. if-theory of algebraically closed fields 509
§2. The e-invariant of a field 516
Contents
vii
§3. The K-theory of M 523
§4. Relation to motivic cohomology 527
§5. K3 of a field 536
§6. Global fields of finite characteristic 552
§7. Local fields 558
§8. Number fields at primes where cd = 2 564
§9. Real number fields at the prime 2 568
§10. The if-theory of Z 579
Bibliography 589
Index of notation 599
Index 605
|
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| isbn | 9780821891322 |
| language | English |
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| spelling | Weibel, Charles A. 1950- Verfasser (DE-588)142971200 aut The K-book an introduction to algebraic K-theory Charles A. Weibel Providence, RI American Math. Soc. 2013 XII, 618 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 145 K-theory K-theory -- General reference works (handbooks, dictionaries, bibliographies, etc.) msc K-theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-0943-2 Graduate studies in mathematics 145 (DE-604)BV009739289 145 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025959507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weibel, Charles A. 1950- The K-book an introduction to algebraic K-theory Graduate studies in mathematics K-theory K-theory -- General reference works (handbooks, dictionaries, bibliographies, etc.) msc K-theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4141839-6 |
| title | The K-book an introduction to algebraic K-theory |
| title_auth | The K-book an introduction to algebraic K-theory |
| title_exact_search | The K-book an introduction to algebraic K-theory |
| title_full | The K-book an introduction to algebraic K-theory Charles A. Weibel |
| title_fullStr | The K-book an introduction to algebraic K-theory Charles A. Weibel |
| title_full_unstemmed | The K-book an introduction to algebraic K-theory Charles A. Weibel |
| title_short | The K-book |
| title_sort | the k book an introduction to algebraic k theory |
| title_sub | an introduction to algebraic K-theory |
| topic | K-theory K-theory -- General reference works (handbooks, dictionaries, bibliographies, etc.) msc K-theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | K-theory K-theory -- General reference works (handbooks, dictionaries, bibliographies, etc.) K-theory -- Instructional exposition (textbooks, tutorial papers, etc.) Algebraische K-Theorie |
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