Dr. Bernd Kreußler

Seminar:
Homological Algebra and
Homological Methods in Commutative Algebra

Beginning:
14 April 1998
End:
17 July 1998
Supplement:
28 September - 2 October 1998
Contents:
Basic Constructions
  1. Derived Functors
    (20+27 April 1998, F. Bunke)
  2. Spectral Sequences
    (4+11+18 May 1998, M. Schulze)
  3. Cohomology of Lie Algebras
    (13 July 1998, V. Levandovsky)
Regular Sequences and the Koszul Complex
  1. Koszul Complexes
    (25 May 1998, T. Mühlhaus)
  2. Duality and Homotopies
    (8 June 1998, E. Westenberger)
Depth, Codimension, and Cohen-Macaulay Rings
  1. Depth, Cohen-Macaulay Rings
    (15 June 1998, M. Maican)
  2. Primeness, Flatness and Depth
    (22 June 1998, I. Kashuba)
Homological Theory of Regular Local Rings
  1. Projective Dimension
    (29 June 1998, A. Getmanenko)
  2. Auslander-Buchsbaum Formula and Factoriality of Regular Local Rings
    (6 July 1998, A. Getmanenko)
Free Resolutions and Fitting Invariants
  1. Fitting Ideals
    (28 September 1998, I. Kashuba)
  2. Hilbert-Burch Theorem
    (28 September 1998, A. Frühbis-Krüger)
  3. Castelnuovo-Mumford Regularity
    (29 September 1998, A. Frühbis-Krüger)
Duality, Canonical Modules, and Gorenstein Rings
  1. Duality
    (29 September 1998, J. Zintl)
  2. Gorenstein Rings
    (1 October 1998, J. Zintl)
  3. Maximal Cohen-Macaulay Modules
    (1 October 1998, T. Keilen)
  4. Duality for MCM
    (2 October 1998, T. Bayer)
  5. Linkage and Cayley-Bacharach Theorems
    (2 October 1998, B. Kreußler)

Recommendable Literature:
W. Bruns, J. Herzog: Cohen-Macaulay rings, Cambridge Univ. Pr., 1993
H. Cartan, S. Eilenberg: Homological Algebra, London : Cumberlege, 1956
D. Eisenbud: Commutative Algebra, Springer, Corrected second printing, 1996 (Corrections) (Our corrections to the second printing 1996)
D. Eisenbud, M. Green, J. Harris: Cayley-Bacharach Theorems and Conjectures; Bull. AMS 33 (1996) 295-324
S. Gelfand, Y. Manin: Methods of Homological Algebra, 1996
R. Godement: Topologie algébrique et théorie des faisceaux, Paris : Hermann, 1973
R. Hartshorne: Algebraic Geometry, Springer 1977
H. Matsumura: Commutative Ring Theory, Cambridge Univ. Pr., 1986
D. Northcott: Homological Algebra, Cambridge Univ. Pr., 1972