General Information for Math 537
Fall 2018
Instructor:

Saul Lubkin
Office: Hylan 705
Email: lubkin@math.rochester.edu
Office Hours: TBA, and also by email
Text: P.J. Hilton and U. Stammbach A Course in Homological Algebra

The book is freely available on-line to UR faculty and students:

A Course in Homological Algebra

The text is excellent. I recommend aquiring a hardcopy as a permanent reference.

Class Meetings: Place: TBA; possibly Hylan 1104
Time: TBA; possibly MW 10:25 -- 11:40
Rough Course Outline


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We'll cover the category of R-modules, abelian categories in general, injective and projective objects, derived functors and some applications, including the special cases of Ext and Tor. We'll then proceed to develop the theory of spectral sequences, using the elegant tool of exact couples introduced by Massey. We'll cover the Grothendieck Spectral Sequence (which is actually a special case of the Cartan-Eilenberg Spectral Sequence of a Composite functor), the spectral sequence of filtered module and the two spectral sequences of a double complex. Applications will be presented as time permits -- most likely, we'll discuss sheaves, cohomology of sheaves and the Leray Spectral Sequence, used in both algebraic topology and algebraic geometry.

Concerning the time and place for this course: It is currently scheduled to meet MW from 10:25-11:40AM; but, we will change that, if useful, to a meeting time better suited for the attendees. So, the initial meeting will actually be an organizational meeting. If you are interested in attending, but can't make that time, please email me what times are good for you.