Thomas Markwig Commutative Algebra
Research Interests
Curriculum Vitae


Seminar: Di, 13:45-15:15, Rm 48-438


  1. Each participant should have studied the Chapters A 2.2-3 and A 3.1-11 in the appendix of David Eisenbud's book.
  2. 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.


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.


Eisenbud: Commutative Algebra with a View towards Algebraic Geometry.
Gelfand, Manin: Methods of Homological Algebra.
Atiyah, MacDonald Introduction to Commutative Algebra.
Hilton, Stammbach: A Course in Homological Algebra.
Matsumura: Commutative Ring Theory.
Markwig: Some Remarks on the Graded Lemma of Nakayama, PS, PDF.

Here you can download the following table as PS-File.


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