Extended Local Cohomology and Local Homology
Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Dual...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sather-Wagstaff, Sean [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Algebras and representation theory - Springer Netherlands, 1998, 19(2016), 5 vom: 11. Mai, Seite 1217-1238 |
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| Übergeordnetes Werk: |
volume:19 ; year:2016 ; number:5 ; day:11 ; month:05 ; pages:1217-1238 |
| Links: |
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| DOI / URN: |
10.1007/s10468-016-9616-5 |
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OLC2036441203 |
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| 520 | |a Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. | ||
| 650 | 4 | |a Adic finiteness | |
| 650 | 4 | |a Cohomologically cofinite complexes | |
| 650 | 4 | |a Derived local cohomology | |
| 650 | 4 | |a Derived local homology | |
| 650 | 4 | |a Greenlees-May duality | |
| 650 | 4 | |a MGM equivalence | |
| 650 | 4 | |a Support | |
| 700 | 1 | |a Wicklein, Richard |4 aut | |
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10.1007/s10468-016-9616-5 doi (DE-627)OLC2036441203 (DE-He213)s10468-016-9616-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik bkl 31.21$jGruppentheorie bkl Sather-Wagstaff, Sean verfasserin aut Extended Local Cohomology and Local Homology 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. Adic finiteness Cohomologically cofinite complexes Derived local cohomology Derived local homology Greenlees-May duality MGM equivalence Support Wicklein, Richard aut Enthalten in Algebras and representation theory Springer Netherlands, 1998 19(2016), 5 vom: 11. Mai, Seite 1217-1238 (DE-627)254285066 (DE-600)1463085-0 (DE-576)081894716 1386-923X nnns volume:19 year:2016 number:5 day:11 month:05 pages:1217-1238 https://doi.org/10.1007/s10468-016-9616-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4310 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik VZ 106418971 (DE-625)106418971 31.21$jGruppentheorie VZ 106408445 (DE-625)106408445 AR 19 2016 5 11 05 1217-1238 |
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10.1007/s10468-016-9616-5 doi (DE-627)OLC2036441203 (DE-He213)s10468-016-9616-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik bkl 31.21$jGruppentheorie bkl Sather-Wagstaff, Sean verfasserin aut Extended Local Cohomology and Local Homology 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. Adic finiteness Cohomologically cofinite complexes Derived local cohomology Derived local homology Greenlees-May duality MGM equivalence Support Wicklein, Richard aut Enthalten in Algebras and representation theory Springer Netherlands, 1998 19(2016), 5 vom: 11. Mai, Seite 1217-1238 (DE-627)254285066 (DE-600)1463085-0 (DE-576)081894716 1386-923X nnns volume:19 year:2016 number:5 day:11 month:05 pages:1217-1238 https://doi.org/10.1007/s10468-016-9616-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4310 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik VZ 106418971 (DE-625)106418971 31.21$jGruppentheorie VZ 106408445 (DE-625)106408445 AR 19 2016 5 11 05 1217-1238 |
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10.1007/s10468-016-9616-5 doi (DE-627)OLC2036441203 (DE-He213)s10468-016-9616-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik bkl 31.21$jGruppentheorie bkl Sather-Wagstaff, Sean verfasserin aut Extended Local Cohomology and Local Homology 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. Adic finiteness Cohomologically cofinite complexes Derived local cohomology Derived local homology Greenlees-May duality MGM equivalence Support Wicklein, Richard aut Enthalten in Algebras and representation theory Springer Netherlands, 1998 19(2016), 5 vom: 11. Mai, Seite 1217-1238 (DE-627)254285066 (DE-600)1463085-0 (DE-576)081894716 1386-923X nnns volume:19 year:2016 number:5 day:11 month:05 pages:1217-1238 https://doi.org/10.1007/s10468-016-9616-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4310 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik VZ 106418971 (DE-625)106418971 31.21$jGruppentheorie VZ 106408445 (DE-625)106408445 AR 19 2016 5 11 05 1217-1238 |
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Sather-Wagstaff, Sean |
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Algebras and representation theory |
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Algebras and representation theory |
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eng |
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2016 |
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Sather-Wagstaff, Sean Wicklein, Richard |
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Aufsätze |
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Sather-Wagstaff, Sean |
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510 |
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extended local cohomology and local homology |
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Extended Local Cohomology and Local Homology |
| abstract |
Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. © Springer Science+Business Media Dordrecht 2016 |
| abstractGer |
Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. © Springer Science+Business Media Dordrecht 2016 |
| abstract_unstemmed |
Abstract We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat {R}^{\mathcal {a}}$ of a commutative noetherian ring R with respect to a proper ideal $\mathcal {a}$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat {R}^{\mathcal {a}}$, not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors. © Springer Science+Business Media Dordrecht 2016 |
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Extended Local Cohomology and Local Homology |
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https://doi.org/10.1007/s10468-016-9616-5 |
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