Local cohomology: an algebraic introduction with geometric applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 2. ed. |
| Series: | Cambridge studies in advanced mathematics
136 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. - Originally published: 1998 |
| Physical Description: | XXII, 491 S. Ill. |
| ISBN: | 9780521513630 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040923888 | ||
| 003 | DE-604 | ||
| 005 | 20140514 | ||
| 007 | t | ||
| 008 | 130403s2013 a||| |||| 00||| eng d | ||
| 020 | |a 9780521513630 |9 978-0-521-51363-0 | ||
| 035 | |a (OCoLC)819496893 | ||
| 035 | |a (DE-599)BVBBV040923888 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-20 |a DE-91G |a DE-19 |a DE-11 | ||
| 082 | 0 | |a 512.55 | |
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 084 | |a SK 320 |0 (DE-625)143231: |2 rvk | ||
| 084 | |a MAT 130f |2 stub | ||
| 084 | |a MAT 143f |2 stub | ||
| 100 | 1 | |a Brodmann, Markus P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Local cohomology |b an algebraic introduction with geometric applications |c M. P. Brodmann ; R. Y. Sharp |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a XXII, 491 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 136 | |
| 500 | |a Includes bibliographical references and index. - Originally published: 1998 | ||
| 650 | 0 | 7 | |a Homologische Algebra |0 (DE-588)4160598-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lokale Kohomologie |0 (DE-588)4168108-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lokale Kohomologie |0 (DE-588)4168108-3 |D s |
| 689 | 0 | 1 | |a Homologische Algebra |0 (DE-588)4160598-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sharp, Rodney Y. |e Verfasser |4 aut | |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 136 |w (DE-604)BV000003678 |9 136 | |
| 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=025902986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025902986 | ||
Record in the Search Index
| _version_ | 1804150219979358208 |
|---|---|
| adam_text | Contents
Preface
to the First Edition page
xi
Preface to the Second Edition xvu
Notation and, conventions
xxi
The local cohomology functors
1
1.1
Torsion functors
1
1.2
Local cohomology modules
3
1.3
Connected sequences of functors
10
Torsion modules and ideal transforms
16
2.1
Torsion modules
17
2.2
Ideal transforms and generalized ideal transforms
21
2.3
Geometrical significance
39
The Mayer-Vietoris sequence
47
3.1
Comparison of systems of ideals
48
3.2
Construction of the sequence
51
3.3
Arithmetic rank
55
3.4
Direct limits
59
Change of rings
65
4.1
Some acyclic modules
66
4.2
The Independence Theorem
70
4.3
The Flat Base Change Theorem
74
Other approaches
81
5.1
Use of
Čech
complexes
82
5.2
Use of
Koszul
complexes
94
5.3
Local cohomology
m
prime characteristic
101
Fundamental vanishing theorems
106
6.1
Grothendieck s Vanishing Theorem
107
viii Contents
6.2
Connections with
grade
112
6.3
Exactness of ideal transforms
117
6.4
An Affineness Criterion due to
Serre
122
6.5
Applications to local algebra
m
prime characteristic
127
7
Artinian local cohomology modules
135
7.1
Artmian modules
135
7.2
Secondary representation
139
7.3
The Non-vanishing Theorem again
143
8
The
Lieh
tenbaum-Hartshorne Theorem
147
8.1
Preparatory lemmas
148
8.2
The mam theorem
156
9
The Annihilator and Finiteness Theorems
164
9.1
Fmiteness dimensions
164
9.2
Adjusted depths
168
9.3
The first inequality
171
9.4
The second inequality
176
9.5
The main theorems
183
9.6
Extensions
188
10
Matlis duality
193
10.1
Indecomposable injective modules
193
10.2
Maths
duality
199
11
Local duality
211
11.1
Minimal mjective resolutions
212
11.2
Local Duality Theorems
216
12
Canonical modules
223
12.1
Definition and basic properties
224
12.2
The endomorphism ring
238
12.3
Ą-ifications
245
13
Foundations in the graded case
251
13.1
Basic multi-graded commutative algebra
253
13.2 *
Injective modules
257
13.3
The ♦restriction property
261
13.4
The reconciliation
271
13.5
Some examples and applications
274
14
Graded versions of basic theorems
285
14.1
Fundamental theorems
286
14.2 *
Indecomposable *mjective modules
295
14.3
A graded version of the Anmhilator Theorem
302
Contents ix
14.4
Graded local duality
309
14.5
Canonical modules
313
15
Links with
projective
varieties
331
15.1 Affine
algebraic cones
331
15.2
Projective varieties
336
16
Castelnuovo regularity
346
16.1
Finitely generated components
346
16.2
The basics of Castelnuovo regularity
351
16.3
Degrees of generators
358
17
Hubert polynomials
364
17.1
The characteristic function
366
17.2
The significance of
reg2 373
17.3
Bounds on
reg2
m
terms of Hubert coefficients
378
17.4
Bounds on
reg1
and
reg0 383
18
Applications to reductions of ideals
388
18.1
Reductions and integral closures
388
18.2
The analytic spread
393
18.3
Links with Castelnuovo regularity
397
19
Connectivity in algebraic varieties
405
19.1
The connectedness dimension
406
19.2
Complete local nngs and connectivity
410
19.3
Some local dimensions
416
19.4
Connectivity of
affine
algebraic cones
422
19.5
Connectivity of projective varieties
424
19.6
Connectivity of intersections
426
19.7
The projective spectrum and connectedness
432
20
Links with sheaf cohomology
438
20.1
The Dehgne Isomorphism
439
20.2
The Graded Deligne Isomorphism
452
20.3
Links with sheaf theory
455
20.4
Applications to projective schemes
465
20.5
Locally free sheaves
476
References
480
Index
485
|
| any_adam_object | 1 |
| author | Brodmann, Markus P. Sharp, Rodney Y. |
| author_facet | Brodmann, Markus P. Sharp, Rodney Y. |
| author_role | aut aut |
| author_sort | Brodmann, Markus P. |
| author_variant | m p b mp mpb r y s ry rys |
| building | Verbundindex |
| bvnumber | BV040923888 |
| classification_rvk | SK 300 SK 320 |
| classification_tum | MAT 130f MAT 143f |
| ctrlnum | (OCoLC)819496893 (DE-599)BVBBV040923888 |
| 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 | 3512.55 |
| 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>01830nam a2200445 cb4500</leader><controlfield tag="001">BV040923888</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20140514 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130403s2013 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521513630</subfield><subfield code="9">978-0-521-51363-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)819496893</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040923888</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.55</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">SK 320</subfield><subfield code="0">(DE-625)143231:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 130f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 143f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brodmann, Markus P.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Local cohomology</subfield><subfield code="b">an algebraic introduction with geometric applications</subfield><subfield code="c">M. P. Brodmann ; R. Y. Sharp</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXII, 491 S.</subfield><subfield code="b">Ill.</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">Cambridge studies in advanced mathematics</subfield><subfield code="v">136</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index. - Originally published: 1998</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Homologische Algebra</subfield><subfield code="0">(DE-588)4160598-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lokale Kohomologie</subfield><subfield code="0">(DE-588)4168108-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lokale Kohomologie</subfield><subfield code="0">(DE-588)4168108-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Homologische Algebra</subfield><subfield code="0">(DE-588)4160598-6</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">Sharp, Rodney Y.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">136</subfield><subfield code="w">(DE-604)BV000003678</subfield><subfield code="9">136</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=025902986&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:BVB01-025902986</subfield></datafield></record></collection> |
| id | DE-604.BV040923888 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:27Z |
| institution | BVB |
| isbn | 9780521513630 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025902986 |
| oclc_num | 819496893 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| physical | XXII, 491 S. Ill. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Brodmann, Markus P. Verfasser aut Local cohomology an algebraic introduction with geometric applications M. P. Brodmann ; R. Y. Sharp 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2013 XXII, 491 S. Ill. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 136 Includes bibliographical references and index. - Originally published: 1998 Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Lokale Kohomologie (DE-588)4168108-3 gnd rswk-swf Lokale Kohomologie (DE-588)4168108-3 s Homologische Algebra (DE-588)4160598-6 s DE-604 Sharp, Rodney Y. Verfasser aut Cambridge studies in advanced mathematics 136 (DE-604)BV000003678 136 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025902986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brodmann, Markus P. Sharp, Rodney Y. Local cohomology an algebraic introduction with geometric applications Cambridge studies in advanced mathematics Homologische Algebra (DE-588)4160598-6 gnd Lokale Kohomologie (DE-588)4168108-3 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4168108-3 |
| title | Local cohomology an algebraic introduction with geometric applications |
| title_auth | Local cohomology an algebraic introduction with geometric applications |
| title_exact_search | Local cohomology an algebraic introduction with geometric applications |
| title_full | Local cohomology an algebraic introduction with geometric applications M. P. Brodmann ; R. Y. Sharp |
| title_fullStr | Local cohomology an algebraic introduction with geometric applications M. P. Brodmann ; R. Y. Sharp |
| title_full_unstemmed | Local cohomology an algebraic introduction with geometric applications M. P. Brodmann ; R. Y. Sharp |
| title_short | Local cohomology |
| title_sort | local cohomology an algebraic introduction with geometric applications |
| title_sub | an algebraic introduction with geometric applications |
| topic | Homologische Algebra (DE-588)4160598-6 gnd Lokale Kohomologie (DE-588)4168108-3 gnd |
| topic_facet | Homologische Algebra Lokale Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025902986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT brodmannmarkusp localcohomologyanalgebraicintroductionwithgeometricapplications AT sharprodneyy localcohomologyanalgebraicintroductionwithgeometricapplications |