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## Ingo Runkel

### Advanced Algebra - Winter term 2016/17

Announcements:
• [27.1] The material relevant for exam block 1 is everything up to (and excluding) the definition of Tor in section "5.4 Flat modules" and problem sheets 1-11. Exam block 2 will cover the complete lecture and all problem sheets.
• [17.1] The exam dates are Thu, 16.2, Fri, 17.2 (block 1) and Thu 23.3, Fri 24.3 (block 2). I will send a STiNE mail explaining the procedure to register for the exam.
• [17.1] The list of points for sheets 1-8 can be found below.
• [16.11] There is no lecture and no exercise class on Fri, 23.12. As discussed, the lecture on Fri 23.12, 12-14 has been moved to Tue, 10.1., and will take place 12:15-13:45 in room 432. There will be a volutary exercise class / question-and-answer session on Tue, 17.1., 12:15-13:45 in room 432.
• [8.12] There was a typo in problem 27, it should read "the right T-module S_T", not "the right S-module T_S". This has been fixed.
• [25.10] Starting this Friday (28.10), the exercise class will be moved forward by 15min, i.e. it will take place 16:00-17:30.
Problem sheets:
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

The problem sheets will be put on the webpage on Friday and will be discussed in the problem class the following Friday.

Solutions:
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

Lecture notes:
Mr Weber has been kind enough to make the notes he takes during the course available here [Dropbox link]. I have not verified the notes, please contact Mr Weber if you have comments.

Description:

In this course we will study some advanced concepts in algebra, in particular:
• rings and modules,
• categories and functors, abelian categories,
• some homological algebra, derived functors.
These structures are ubiquitous in modern mathematics and are important tools for anyone who wishes to use algebraic methods in mathematics or in mathematical physics.
A more detailed outline of the material we hope to cover is here: [pdf]
(The actual contents may differ slightly.)

This course is mainly aimed at Masters students in Mathematics and in Mathematical Physics. Per default it will be held in English (but it can be in German if everyone is sufficiently fluent).

Literature:
• Lang, "Algebra", Springer
• Hilton, Stammbach, "A course in homological algebra", Springer
• Jantzen, Schwermer, "Algebra", Springer (in German)

Exam:

To qualify for the exam, you should least 40% of the homework problems and participate actively in the problem classes. At the beginning of each class, you can mark on a list which problems (or problem parts, for longer problems) you solved and can present on the board. To qualify for the exam, you should have marked 40% or more of the problems by the end of the course. If you marked a problem as solved but it becomes apparent that you did not prepare it sufficiently in case you get asked to the board, the all problems for that week will be marked as not solved.
The list of points for sheets 1-8 can be found here: [pdf]. The total number of points in the 12 problem sheets is 12*5=60, and 40% of this is 24. So you need 24 points or more to be admitted to the exam.
The exam itself will be an oral exam. We will decide the dates together later in the course.

 Impressum 2017-01-27, Ingo Runkel