Polytopes, rings, and K-Theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht ; Heidelberg ; London ; New Yok
Springer
[2009]
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 461 Seiten Illustrationen |
| ISBN: | 9780387763552 9780387763569 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035674593 | ||
| 003 | DE-604 | ||
| 005 | 20230214 | ||
| 007 | t | ||
| 008 | 090812s2009 gw a||| |||| 00||| eng d | ||
| 015 | |a 07,N43,0530 |2 dnb | ||
| 016 | 7 | |a 985875003 |2 DE-101 | |
| 020 | |a 9780387763552 |c print |9 978-0-387-76355-2 | ||
| 020 | |a 9780387763569 |c online |9 978-0-387-76356-9 | ||
| 035 | |a (OCoLC)426065881 | ||
| 035 | |a (DE-599)DNB985875003 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-355 |a DE-11 |a DE-83 |a DE-188 |a DE-20 | ||
| 050 | 0 | |a QA612.32 | |
| 082 | 0 | |a 512.6 |2 22 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 084 | |a 19Dxx |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Bruns, Winfried |d 1946- |0 (DE-588)171993454 |4 aut | |
| 245 | 1 | 0 | |a Polytopes, rings, and K-Theory |c Winfried Bruns ; Joseph Gubeladze |
| 264 | 1 | |a Dordrecht ; Heidelberg ; London ; New Yok |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a XIII, 461 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 650 | 4 | |a K-theory | |
| 650 | 4 | |a Polytopes | |
| 650 | 4 | |a Rings (Algebra) | |
| 650 | 0 | 7 | |a K-Theorie |0 (DE-588)4033335-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ringtheorie |0 (DE-588)4126571-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexes Polytop |0 (DE-588)4367579-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexes Polytop |0 (DE-588)4367579-7 |D s |
| 689 | 0 | 1 | |a Ringtheorie |0 (DE-588)4126571-3 |D s |
| 689 | 0 | 2 | |a K-Theorie |0 (DE-588)4033335-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gubeladze, Joseph |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-76356-9 |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3010137&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 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=017728817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017728817 | |
Datensatz im Suchindex
| _version_ | 1805092758850895872 |
|---|---|
| adam_text |
Contents
Part I Cones, monoids, and
triangulations
1
Polytopes, cones, and complexes
. 3
LA Polyhedra and their faces
. 3
l.B Finite generation of cones
. 10
l.C Finite generation of polyhedra
. 15
l.D Polyhedral complexes
. 21
l.E Subdivisions and
triangulations
. 25
l.F Regular subdivisions
. 31
l.G Rationality and integrality
. 39
Exercises
. 44
Notes
. 47
2
Affine
monoids and their Hilbert bases
. 49
2.A
Affine
monoids
. 49
2.B Normal
affine
monoids
. 58
2.C Generating normal
affine
monoids
. 67
2.D Normality and unimodular covering
. 77
Exercises
. 85
Notes
. 88
3
Multiples of lattice polytopes
. 91
3.A Knudsen-Mumford
triangulations
. 91
3.B Unimodular
triangulations
of multiples of polytopes
. 97
3.C Unimodular covers of multiples of polytopes
. 103
Exercises
. 117
Notes
. 119
XII Contents
Part II
Affine
monoid algebras
4
Monoid algebras
. 123
4.A Graded rings
. 123
4.B Monoid algebras
. 129
4.C Representations of monoid algebras
. 133
4.D Monomial prime and radical ideals
. 137
4.E Normality
. 140
4.F Divisorial ideals and the class group
. 145
4.G The
Picard
group and seminormality
. 153
Exercises
.160
Notes
. 162
5
Isomorphisms and automorphisms
. 165
5.A Linear algebraic groups
. 165
5.B Invariants of diagonalizable groups
. 172
5.C The isomorphism theorem
. 175
5.D Automorphisms
. 183
Exercises
. 195
Notes
. 198
6
Homological properties and Hilbert functions
. 199
6.A Cohen-Macaulay rings
. 199
6.B Graded homological algebra
.206
6.C The canonical module
.213
6.D Hilbert functions
.218
6.E Applications to enumerative combinatorics
.227
6.F Divisorial linear algebra
.237
Exercises
. 246
Notes
. 248
7 Gröbner
bases,
triangulations,
and
Koszul
algebras
.251
7.A
Gröbner
bases and initial ideals
. 251
7.B Initial ideals of toric ideals
.256
7.C Toric ideals and
triangulations
.267
7.D Multiples of lattice polytopes
.276
Exercises
. 281
Notes
. 282
Contents XIII
Partili
K-theory
8
Projective
modules
over monoid rings
.287
8.A
Projective
modules
.287
8.B The main theorem and the plan of the proof
.289
8.C
Projective
modules over polynomial rings
.292
8.D Reduction to the interior
.297
8.E Graded
"Weierstrass
preparation"
.298
8.F Pyramidal descent
.299
8.G How to shrink a polytope
.305
8.H Converse results
.307
8.1
Generalizations
.309
Exercises
.321
Notes
.324
9
Bass-Whitehead groups of monoid rings
.327
9.A The functors Ki and K2
.327
9.B The nontriviality of SKi(R[M])
.333
9.C Further results: a survey
.345
Exercises
.351
Notes
.353
10
Varieties
.355
10.A Vector bundles, coherent sheaves, and Grothendieck groups
.356
10.B Toric varieties
.364
10.C Chow groups of toric varieties
.375
10.D Intersection theory
.380
10.E Chow cohomology of toric varieties
.393
10.
F
Toric varieties with huge Grothendieck group
.404
10.G The equivariant
Serre
problem for abelian groups
.413
Exercises
.425
References
.429
Notation
.445
Index
.451 |
| any_adam_object | 1 |
| author | Bruns, Winfried 1946- Gubeladze, Joseph |
| author_GND | (DE-588)171993454 |
| author_facet | Bruns, Winfried 1946- Gubeladze, Joseph |
| author_role | aut aut |
| author_sort | Bruns, Winfried 1946- |
| author_variant | w b wb j g jg |
| building | Verbundindex |
| bvnumber | BV035674593 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.32 |
| callnumber-search | QA612.32 |
| callnumber-sort | QA 3612.32 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 300 |
| ctrlnum | (OCoLC)426065881 (DE-599)DNB985875003 |
| dewey-full | 512.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.6 |
| dewey-search | 512.6 |
| dewey-sort | 3512.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV035674593</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230214</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090812s2009 gw a||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">07,N43,0530</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">985875003</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387763552</subfield><subfield code="c">print</subfield><subfield code="9">978-0-387-76355-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387763569</subfield><subfield code="c">online</subfield><subfield code="9">978-0-387-76356-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)426065881</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB985875003</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612.32</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.6</subfield><subfield code="2">22</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">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">19Dxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bruns, Winfried</subfield><subfield code="d">1946-</subfield><subfield code="0">(DE-588)171993454</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Polytopes, rings, and K-Theory</subfield><subfield code="c">Winfried Bruns ; Joseph Gubeladze</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht ; Heidelberg ; London ; New Yok</subfield><subfield code="b">Springer</subfield><subfield code="c">[2009]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 461 Seiten</subfield><subfield code="b">Illustrationen</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="0" ind2=" "><subfield code="a">Springer monographs in mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">K-theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polytopes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rings (Algebra)</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">Ringtheorie</subfield><subfield code="0">(DE-588)4126571-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexes Polytop</subfield><subfield code="0">(DE-588)4367579-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Konvexes Polytop</subfield><subfield code="0">(DE-588)4367579-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Ringtheorie</subfield><subfield code="0">(DE-588)4126571-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">K-Theorie</subfield><subfield code="0">(DE-588)4033335-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gubeladze, Joseph</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-0-387-76356-9</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3010137&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=017728817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017728817</subfield></datafield></record></collection> |
| id | DE-604.BV035674593 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:16:42Z |
| institution | BVB |
| isbn | 9780387763552 9780387763569 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017728817 |
| oclc_num | 426065881 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-83 DE-188 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 DE-188 DE-20 |
| physical | XIII, 461 Seiten Illustrationen |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Bruns, Winfried 1946- (DE-588)171993454 aut Polytopes, rings, and K-Theory Winfried Bruns ; Joseph Gubeladze Dordrecht ; Heidelberg ; London ; New Yok Springer [2009] © 2009 XIII, 461 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics K-theory Polytopes Rings (Algebra) K-Theorie (DE-588)4033335-8 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Konvexes Polytop (DE-588)4367579-7 gnd rswk-swf Konvexes Polytop (DE-588)4367579-7 s Ringtheorie (DE-588)4126571-3 s K-Theorie (DE-588)4033335-8 s DE-604 Gubeladze, Joseph aut Erscheint auch als Online-Ausgabe 978-0-387-76356-9 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3010137&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruns, Winfried 1946- Gubeladze, Joseph Polytopes, rings, and K-Theory K-theory Polytopes Rings (Algebra) K-Theorie (DE-588)4033335-8 gnd Ringtheorie (DE-588)4126571-3 gnd Konvexes Polytop (DE-588)4367579-7 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4126571-3 (DE-588)4367579-7 |
| title | Polytopes, rings, and K-Theory |
| title_auth | Polytopes, rings, and K-Theory |
| title_exact_search | Polytopes, rings, and K-Theory |
| title_full | Polytopes, rings, and K-Theory Winfried Bruns ; Joseph Gubeladze |
| title_fullStr | Polytopes, rings, and K-Theory Winfried Bruns ; Joseph Gubeladze |
| title_full_unstemmed | Polytopes, rings, and K-Theory Winfried Bruns ; Joseph Gubeladze |
| title_short | Polytopes, rings, and K-Theory |
| title_sort | polytopes rings and k theory |
| topic | K-theory Polytopes Rings (Algebra) K-Theorie (DE-588)4033335-8 gnd Ringtheorie (DE-588)4126571-3 gnd Konvexes Polytop (DE-588)4367579-7 gnd |
| topic_facet | K-theory Polytopes Rings (Algebra) K-Theorie Ringtheorie Konvexes Polytop |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3010137&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brunswinfried polytopesringsandktheory AT gubeladzejoseph polytopesringsandktheory |