General Information
for Math 537 Fall 2018 | ||
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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
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A Course in Homological Algebra
The text is excellent. I recommend aquiring a hardcopy as a permanent reference. |
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Class Meetings: | Place: | TBA; possibly Hylan 1104 |
Time: | TBA; possibly MW 10:25 -- 11:40 | |
Rough Course Outline | ||
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.
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