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Lecture 24 : Tor, the left derived functor of the tensor product. Lecture 25 : Long exact sequence of left derived functors. We covered most of Section 7. The naturality of the connecting homomorphism in Theorem 34 was stated but the proof was left as an exercise, the same is true of Proposition 37 and Proposition 38 I stated but did not prove them.
Finally we discussed that the natural transformations induced on derived functors by Definition 9 are used to make Tor a bifunctor, for which see p. Lecture 26 : Right derived functors and Ext.
We covered Section 7. Lecture 27 : Projective dimension and global dimension. For more background see my other notes on Homological dimensions. Lecture 28 : Global dimension for Noetherian local rings. Lecture 3 Exercise 2. Lecture 5 Exercise 3, 4.
Read Sheaves And Homological Algebra Lecture 1 Lecture Notes
Lecture 6 Exercises 1, 2. Assignment 2 due Tuesday 4th October in class : Lecture 10 Exercise 2. Lecture 11 Exercises 5,6. Lecture 12 Exercise 1. Lecture 13 Exercises 1,2. Copyright Year: Page Count: Cover Type: Hardcover. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: 55 ; Applied Math?
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Apparel or Gift: false. Online Price 1 Label: List. Online Price 1: Print Price 1 Label: List. Print Price 1: Online Price 2: Print Price 2: Weibel, An introduction to homological algebra. As I take it for the first time, the lecture notes will progressively be available in the course of the semester.
I will correct them. Comments and suggestions are also welcome.
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What is Group Cohomology by Peter Webb. In principle one should be able to explain the content of the lecture notes. There won't be questions on the last lecture either. Please, be ready to write down formally the concepts and results you are explaining. Contents of the Lecture Semidirect products of groups Presentations of groups Homological algebra Homology and cohomology of groups Cohomology and group extensions The Schur multiplier and central extensions Projective representations Prerequisites : elementary group theory and linear algebra.
Lecture : 4 SWS, i. Patrick Wegener.