Algebraic K-theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1996
|
| Edition: | 2. ed. |
| Series: | Progress in mathematics
90 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 339 - 431 |
| Physical Description: | XVI, 341 S. |
| ISBN: | 3764337028 0817637028 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010613250 | ||
| 003 | DE-604 | ||
| 005 | 19960802 | ||
| 007 | t | ||
| 008 | 960129s1996 gw |||| 00||| ger d | ||
| 016 | 7 | |a 946468443 |2 DE-101 | |
| 020 | |a 3764337028 |c (Basel ...) Pp. : sfr 98.00 |9 3-7643-3702-8 | ||
| 020 | |a 0817637028 |c (Boston ...) Pp. |9 0-8176-3702-8 | ||
| 035 | |a (OCoLC)27432870 | ||
| 035 | |a (DE-599)BVBBV010613250 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-29T |a DE-91 |a DE-19 |a DE-355 |a DE-11 | ||
| 050 | 0 | |a QA612.33 | |
| 082 | 0 | |a 512/.55 |2 20 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a MAT 552f |2 stub | ||
| 084 | |a MAT 189f |2 stub | ||
| 100 | 1 | |a Srinivas, V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic K-theory |c V. Srinivas |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1996 | |
| 300 | |a XVI, 341 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 90 | |
| 500 | |a Literaturverz. S. 339 - 431 | ||
| 650 | 7 | |a Algebra homologica |2 larpcal | |
| 650 | 4 | |a K-theory | |
| 650 | 0 | 7 | |a K-Theorie |0 (DE-588)4033335-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a K-Theorie |0 (DE-588)4033335-8 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 689 | 2 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 830 | 0 | |a Progress in mathematics |v 90 |w (DE-604)BV000004120 |9 90 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007080863 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804125088546553857 |
|---|---|
| adam_text | Contents
Preface to the First Edition xi
Preface to the Second Edition xvii
1. Classical /( Theory 1
Review of parts of Milnor s book: definitions of Kg, K , K2 of rings;
computation of K of a noncommutative local ring; definition of sym¬
bols; statement of Matsumoto s theorem; examples of symbols (norm
residue symbol, Galois symbol, differential symbol); presentation for
A 2 of a commutative local ring.
2. The Plus Construction 18
The plus construction; computation that n2{BGL(R)^) S K2(fl);
// space structure of BGL(R)* and products in A theory (following
Loday); statement of Quillen s theorem on K of a finite field.
3. The Classifying Space of a Small Category 31
Simplicial sets; geometric realization; classifying space of a small cate¬
gory; elementary theorems about classifying spaces (compatibility with
products, natural transformations give homotopies, adjoint functors
give homotopy inverses, filtering categories are contractible); example
of the classifying space of a discrete group as the classifying space of
the category with one object, whose endomorphisms equal the group.
4. Exact Categories and Quillen s Q Construction 38
Exact categories; admissible mono and epimorphisms; definition of
QC for a small exact category C; definition of Ki(C) for a small ex¬
act category C; statements of theorems about K, (Ko agrees with that
defined classically , theorem on exact sequences of functors, resolu¬
tion theorem, devissage theorem, localization theorem); bare hands
construction of a homomorphism Ka{C) —» Tt BQC).
viii Algebraic ff Theory
5. The /( Theory of Rings and Schemes 46
Statement of the theorem comparing the definitions of Ki of a ring using
the plus and Q constructions; definition of Gi(A) as Ki of finitely gen¬
erated /1 modules, for Noetherian rings A; computations of Gj( 4[ ]),
GiiAlt.t 1]) for Noetherian A, and hence Ki(A t]), Ki(A t,t~ ]) for
Noetherian regular A; definition of Ki(X), Gi(X) for schemes, using
vector bundles and coherent sheaves, respectively; construction of di¬
rect image and inverse image maps for Ki and Gi of Noetherian schemes
for morphisms satisfying appropriate conditions; action of Ko on Ki,
G, and projection formulas; Ki, Gi commute with filtered direct lim¬
its; localization for G, of a closed subscheme and the open complement;
Mayer Vietoris for Gc, Gi of affine and projective space bundles; fil¬
tration by codimension of support and (he BGQ spectral sequence;
Gersten s conjecture for power series rings, and semilocal rings of fi¬
nite sets of points on a smooth variety over an infinite field; Bloch s
formula; Ki of projective bundles, of P over a noncommutative ring,
and of Severi Brauer schemes.
6. Proofs of the Theorems of Chapter 4 89
Proofs of the following theorems: mBQC) S K0(C); Theorems A and B
of Quillen; the theorem on exact sequences of functors; the resolution
theorem; the devissage theorem; the localization theorem.
7. Comparison of the Plus and Q Constructions 126
Monoidal categories; localization of the action of a monoida) category
on a small category; computation of the homology of the classifying
space of a localized category; the S~ S construction, viewed as a func
torial version of the plus construction; construction of the homotopy
equivalence S~ S — QBQC for any exact category C in which all ex¬
act sequences are split, where S is the category of isomorphisms in C;
corollary that the plus and Q constructions yield the same A groups
for projective modules over a ring.
8. The Merkurjev Suslin Theorem 145
The Galois symbol; statement of the Mcrkurjev Suslin theorem;
Hilbert s Theorem 90 for Ki; proof of the Merkurjev Suslin theorem;
torsion in Ki torsion in CH2.
9. Localization for Singular Varieties 194
Quillen s localization theorem for the complement of an effective Cartier
divisor in a quasi projective scheme with affine complement; discussion
of naturality of this sequence (after Swan); proof of the Fundamental
Theorem on Ki of polynomial and Laurent polynomial rings; Levine s
localization theorem; computation of Ko of the category of modules
of finite length and finite projective dimension over the local ring of a
normal surface singularity, in terms of H (K2) of the resolution; com¬
putation of this Ko for quotient singularities; Chow groups of surfaces
with quotient singularities.
Contents ix
Appendix A. Results from Topology 230
(A.I) Compactly generated spaces; (A.2) (A.6) Homotopy groups,
Hurewicz theorems; (A.7) Products; (A.8) (A.12) CW complexes,
Whitehead theorem, Milnor s theorem on the homotopy type of map¬
ping spaces, comparison of singular and cellular homology and cohomol
ogy; (A.13) (A.15) Local coefficients, homology and cohomology with
local coefficients for CW complexes via cellular chains; (A. 16) Obstruc¬
tion theory for maps and homotopies between CW complexes (which
may not be simply connected); (A. 17) (A.22) Fibrations, the homotopy
lifting property, long exact homotopy sequence, fiber homotopy equiv¬
alence, fibrations over a contractible base are fiber homotopy equiva¬
lent to a product, local coefficient systems of the homology and coho¬
mology groups of the fibers of a fibration; (A.23) (A.26) Leray Serre
spectral sequence for homology and cohomology of a fibration over a
CW complex; (A.27) Homotopy fibers; (A.28) Spectral sequences for
the homology and cohomology of a covering space; (A.2!)) (A35) Quasi
fibrations (some results of Dold and Thoni); (A.36) (A.42) NDR pairs
and cofibrations (following Steenrod); (A.43) (A.47) // spaces; (A.48)
(A.50) Covering spaces of simplicial sets; (A.51) (A.54) Hurewicz and
Whitehead theorems for non simply connected // spaces; (A.55) Mil¬
nor s theorem on the geometric realization of a product of simplicial
sets.
Appendix B. Results from Category Theory 276
Small categories; equivalences; Abelian categories; construction of the
quotient of a small Abelian category by a Serre subcategory; examples
of quotients; adjoint functors; filtering categories and direct limits.
Appendix C. Exact Couples 287
The spectral sequence of an exact couple; bigraded couples; elementary
discussion of convergence; the BGQ spectral sequence; the spectral
sequence of a filtered complex.
Appendix D. Results from Algebraic Geometry 295
(D.1) (D.14) Sheaves; (D.15) (D.20) Schemes; (D.21) (D.41) Some
properties of schemes; (D.42) (D.59) Coherent and quasi coherent
sheaves; (D.60) (D.66) Cohomology and direct images of quasi coherent
and coherent sheaves; (D.67) (D.7O) Some miscellaneous topics.
Bibliography 339
|
| any_adam_object | 1 |
| author | Srinivas, V. |
| author_facet | Srinivas, V. |
| author_role | aut |
| author_sort | Srinivas, V. |
| author_variant | v s vs |
| building | Verbundindex |
| bvnumber | BV010613250 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.33 |
| callnumber-search | QA612.33 |
| callnumber-sort | QA 3612.33 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| classification_tum | MAT 552f MAT 189f |
| ctrlnum | (OCoLC)27432870 (DE-599)BVBBV010613250 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02107nam a2200565 cb4500</leader><controlfield tag="001">BV010613250</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19960802 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960129s1996 gw |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">946468443</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764337028</subfield><subfield code="c">(Basel ...) Pp. : sfr 98.00</subfield><subfield code="9">3-7643-3702-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817637028</subfield><subfield code="c">(Boston ...) Pp.</subfield><subfield code="9">0-8176-3702-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)27432870</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010613250</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612.33</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.55</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 552f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 189f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Srinivas, V.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic K-theory</subfield><subfield code="c">V. Srinivas</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston ; Basel ; Berlin</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 341 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Progress in mathematics</subfield><subfield code="v">90</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 339 - 431</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebra homologica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">K-theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">K-Theorie</subfield><subfield code="0">(DE-588)4033335-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische K-Theorie</subfield><subfield code="0">(DE-588)4141839-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische K-Theorie</subfield><subfield code="0">(DE-588)4141839-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">K-Theorie</subfield><subfield code="0">(DE-588)4033335-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Progress in mathematics</subfield><subfield code="v">90</subfield><subfield code="w">(DE-604)BV000004120</subfield><subfield code="9">90</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007080863</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV010613250 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:56:00Z |
| institution | BVB |
| isbn | 3764337028 0817637028 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007080863 |
| oclc_num | 27432870 |
| open_access_boolean | |
| owner | DE-29T DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-29T DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 |
| physical | XVI, 341 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Srinivas, V. Verfasser aut Algebraic K-theory V. Srinivas 2. ed. Boston ; Basel ; Berlin Birkhäuser 1996 XVI, 341 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 90 Literaturverz. S. 339 - 431 Algebra homologica larpcal K-theory K-Theorie (DE-588)4033335-8 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s DE-604 K-Theorie (DE-588)4033335-8 s 1\p DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 Progress in mathematics 90 (DE-604)BV000004120 90 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Srinivas, V. Algebraic K-theory Progress in mathematics Algebra homologica larpcal K-theory K-Theorie (DE-588)4033335-8 gnd Algebra (DE-588)4001156-2 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4001156-2 (DE-588)4141839-6 |
| title | Algebraic K-theory |
| title_auth | Algebraic K-theory |
| title_exact_search | Algebraic K-theory |
| title_full | Algebraic K-theory V. Srinivas |
| title_fullStr | Algebraic K-theory V. Srinivas |
| title_full_unstemmed | Algebraic K-theory V. Srinivas |
| title_short | Algebraic K-theory |
| title_sort | algebraic k theory |
| topic | Algebra homologica larpcal K-theory K-Theorie (DE-588)4033335-8 gnd Algebra (DE-588)4001156-2 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | Algebra homologica K-theory K-Theorie Algebra Algebraische K-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT srinivasv algebraicktheory |