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visits | member for | 4 years, 10 months |
seen | Aug 25 at 1:14 | |
stats | profile views | 355 |
Oct 11 |
awarded | Yearling |
Oct 12 |
awarded | Yearling |
Mar 3 |
awarded | Nice Answer |
Nov 18 |
comment |
How to introduce notions of flat, projective and free modules?
@Pete: In my mind, the exactness of the tensor product is relatively easy to motivate through change of rings. Say you've got your sequence over $R$ and you've got an ideal $I$. Is it still exact when we think of everything as $R/I$ modules? Well, that's what the exactness of the tensor product will tell you. Of course this becomes very useful once you have localization and completions to play with. For $Hom$, it seems easiest to motivate $Hom(-,R)$ by analogy with vector space duals, and you can build up from there to $Hom(-,M)$ and $Hom(M,-)$. |
Nov 13 |
awarded | Critic |
Oct 24 |
awarded | Popular Question |
Oct 19 |
awarded | Good Question |
Oct 12 |
awarded | Yearling |
Aug 12 |
answered | A chain homotopy that does not arise from a homotopy of spaces? |
May 30 |
awarded | Nice Answer |
Mar 9 |
awarded | Fanatic |
Dec 31 |
comment |
effective teaching
There is a recent book from the MAA titled "The Moore method : a pathway to learner-centered instruction" that describes five teachers' variations on the Moore method. It may be helpful to look through it for ideas. |
Dec 7 |
awarded | Civic Duty |
Nov 24 |
answered | How to think about CM rings? |
Nov 23 |
awarded | Nice Question |
Nov 19 |
awarded | Enthusiast |
Nov 13 |
comment |
Theorems for nothing (and the proofs for free)
That's quite surprising! What are some good references for this? |
Nov 6 |
comment |
What representative examples of modules should I keep in mind?
@Dinakar: the top part of the picture is a module M. The labels M_P and M_Q denote the localizations at primes. The bottom part of the picture is the ring R, with primes P and Q labeled. The curves drawn in R represent the support of M. Presumably the thicker lines are indicating embedded primes (non-minimal associated primes), and eta is a generic point (non-maximal prime). |
Nov 3 |
answered | Memorizing theorems |
Oct 23 |
comment |
What does a projective resolution mean geometrically?
In my mind, the easiest way for a sheaf to not be locally free is for some point p to lack a local trivialization. For vector bundles I can visualize this happening when the stalks do not vary nicely: at p they change directions suddenly (what I meant by "sharply twisting") or the dimension of the stalks change ("pinching" of some sort). This might be confusing smoothness with local free-ness; I'm not really sure what's going on geometrically - hence my question. I feel like the maps in the resolution can be described geometrically rather than algebraically in some way. I just don't know how. |