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Dates:
Seminar: Di and Mi 13:45-15:15, Rm 48-438
Aktuelles:
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The seminar consists of 17 talks given by the participants. We,
therefore, will have to arrange some extra meetings at the beginning
of the term. These will take place on Wednesdays.
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Each participant should have studied the Chapters A 2.2-3 and A
3.1-11 in the appendix of David Eisenbud's book.
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Each talk should last not more than 90 minutes. Therefore, sometimes
the speaker will have to give just main ideas of a proof rather than
its details. The talk should illustrate the most important results
by illuminating examples.
Contents:
The seminar is a continuation of the lecture commutative algebra
last winter term. The contents include: graded rings and modules;
regular rings; Auslander-Buchsbaum formula; Hilbert's Syzygy Theorem;
Fitting ideals; Theorem of Hilbert-Burch; Castelnuovo-Mumford
regularity; duality; Gorenstein rings; maximal Cohen-Macaulay modules.
Literature:
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Eisenbud: Commutative Algebra with a View towards Algebraic
Geometry.
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Gelfand, Manin: Methods of Homological Algebra.
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Atiyah, MacDonald Introduction to Commutative
Algebra.
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Hilton, Stammbach: A Course in Homological Algebra.
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Matsumura: Commutative Ring Theory.
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Markwig: Some Remarks on the Graded Lemma of Nakayama,
PS,
PDF.
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Here you can download the following table as
PS-File,
PDF-File.
Talks:
| Title | Literature | Speaker | Date |
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| General Reading |
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| 0. | Homological Algebra | Eisenbud, Kap. A 2.2 \& A 3.1-11 | alle |
| Regular Rings, Graded Rings and Modules |
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| 1. | Regular Rings | Eisenbud, Sätze 3.11b, 10.6-9 \& 10.14-15 | Klaus Huthmacher | 26.4.05 |
| 2. | Graded Modules and Rings | Eisenbud, Kap. 1.5, 1.9-10,
A 3.2; + Markwig | Markus Hochstetter | 27.4.05 |
| Regular Sequences and the Koszul Complex |
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| 3. | Koszul Complexes | Eisenbud, Kap. 17.1-4, p.
423-440 | Silke Spang | 3.+4.5.05 |
| Depth, Codimension, and Cohen-Macaulay Rings |
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| 4. | Depth | Eisenbud, Kap. 18.1, p. 451-455 | Lars Allermann | 10.5.05 |
| 5. | Cohen-Macaulay Rings | Eisenbud, Kap. 18.2, p. 455-460 | Mathias Altenhöfer | 24.5.05 |
| 6. | Primeness, Flatness and Depth | Eisenbud, Kap. 18.3-4, p. 461-466 | Eckehard Hollborn | 25.5.05 |
| Homological Theory of Regular Local Rings |
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| 7. | Projective Dimension | Eisenbud, Kap. 19.1-2, p. 473-478 | Marina Franz | 1.6.05 |
| 8. | Auslander-Buchsbaum Formula | Eisenbud, Kap. 19.2-3, p. 478 (C.~19.8)-483 | Thomas Trenner | 7.6.05 |
| 9. | Factoriality of Regular Local Rings | Eisenbud, Kap. 19.3-4, p. 483 (C.~19.14)-487 | Tanja Berger | 14.6.05 |
| Free Resolutions and Fitting Invariants |
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| 10. | Fitting Ideals | Eisenbud, Kap. 20.1-2, p. 489-496 | Zaenal Aripin | 15.6.05 |
| 11. | Hilbert-Burch Theorem | Eisenbud,
Kap. 20.3-4, p. 496-503 | Anne Frühbis-Krüger | 28.6.05 |
| 12. | Castelnuovo-Mumford Regularity | Eisenbud, Kap. 20.4-5, p. 503-510 | Christian Dingler | 5.7.05 |
| Duality, Canonical Modules, and Gorenstein Rings |
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| 13. | Duality | Eisenbud, Kap. 21.1, p. 523-529 | Andreas Gathmann | 12.7.05 |
| 14. | Gorenstein Rings | Eisenbud, Kap. 21.2-3, p. 529-533 | Lesya Bodnarchuk | 13.7.05 |
| 15. | Maximal Cohen-Macaulay Modules | Eisenbud, Kap. 21.4-6, p. 533-540 | Markus Barthlen | 19.7.05 |
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