Exploring the Spectrum of Rings: Analytic & Differentiable Functions

In summary: The spectrum of the ring of continuous functions is always compact, so it cannot be isomorphic to Euclidean n-space.
  • #36
One is the number of handles in the usual topology, which we cannot use, and the other is the number of linearly independent differential forms.

All right, I'll see if I can go from here. Hopefully I won't need to peek!
 
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  • #37
did we switch from here to "more questions on alg geom"?
 
  • #38
I tend to start new posts when I have new questions; I hadn't thought about just keeping them all to one thread...
 
  • #39
sorry this is the only way i can have 15 straight most recentposts, a new record for me.

i feel bad if it totally vacuous though, so here is a toss off question for you. can you show me an example of a ring with infinite krull dimension, but each maximal ideals has finite height?

i.e. each prime ideal represents a subvariety of finite dimension but there are subvarieties of arbitrary dimension?
 
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