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Dates:
Seminar: Di, 13:45-15:15, Rm 48-438
Aktuelles:
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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.
Talks:
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Titel of the Talk |
Literature |
| Lecturer |
Date |
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General Reading |
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0 |
Homological Algebra |
[Eisenbud, Kap. A 2.2 & A 3.1-11] |
| all |
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Regular Rings, Graded Rings and Modules |
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1 |
Regular Rings |
[Eisenbud, Sätze 10.5, 10.7, 10.10 & 10.14-15] |
| Max Pumperla |
25.04.06 |
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2 |
Graded Modules and Rings |
[Eisenbud, Kap. 1.5, 1.9-10], [Atiyah-Macdonald, Prop. 10.7] |
| Stefania Barzan |
02.05.06 |
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3 |
Graded Lemma of Nakayama |
[Markwig], [Atiyah-Macdonald, Thm. 11.22], [Atiyah-Macdonald, 10.8-9] |
| Shawki Al-Rashed |
09.05.06 |
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4 |
Flatness and Tor |
[Eisenbud, Kap. 6.1-2, Prop. 6.1, Cor. 6.3, Thm. 6.8] |
| Matthias Herold |
16.05.06 |
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Regular Sequences and the Koszul Complex |
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5 |
Koszul Complexes |
[Eisenbud, Kap. 17.1-4 pp. 423-440] |
| Thomas Markwig |
23./30.05.06 |
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Depth, Codimension, and Cohen-Macaulay Rings |
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6 |
Depth |
[Eisenbud, Kap. 18.1 pp. 451-455] |
| Maximilian Boy |
13.06.06 |
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7 |
Cohen-Macaulay Rings |
[Eisenbud, Kap. 18.2 pp. 455-460] |
| Andreas Glang |
27.06.06 |
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8 |
Primness, Flatness and Depth |
[Eisenbud, Kap. 18.3-4 pp. 461-466] |
| ??? |
04.07.06 |
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Homological Theory of Regular Local Rings |
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9 |
Projective Dimension |
[Eisenbud, Kap. 19.1-2 pp. 473-478, Thm. 20.1] |
| Clemens Thielen |
11.07.06 |
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10 |
Auslander-Buchsbaum Formula |
[Eisenbud, Kap. 19.2-3 pp. 478 (C. 19.8)-483] |
| Achim Faßbender |
18.07.06 |
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11 |
Factoriality of Regular Rings |
[Eisenbud, Kap. 19.3-4 pp. 483 (C. 19.14)-487] |
| Maryna Viazovska |
25.07.06 |
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