Holdings: Polytopes, rings, and K-Theory

Polytopes, rings, and K-Theory:

Saved in:

Bibliographic Details
Main Authors:	Bruns, Winfried 1946- (Author), Gubeladze, Joseph (Author)
Format:	Book
Language:	English
Published:	Dordrecht ; Heidelberg ; London ; New Yok Springer [2009]
Series:	Springer monographs in mathematics
Subjects:	K-theory Polytopes Rings (Algebra) K-Theorie Ringtheorie Konvexes Polytop
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XIII, 461 Seiten Illustrationen
ISBN:	9780387763552 9780387763569

Staff View

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

Record in the Search Index

_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

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Description

MARC

Record in the Search Index

There is no print copy available.

Similar Items