Reputation
995
Next privilege 1,000 Rep.
Create new tags
Badges
5 12
Impact
~26k people reached

  • 0 posts edited
  • 0 helpful flags
  • 109 votes cast
Jun
18
revised What happens geometrically when the Jacobson radical is non-zero?
added 100 characters in body; added 9 characters in body; added 71 characters in body
Jun
18
revised What happens geometrically when the Jacobson radical is non-zero?
added 135 characters in body; edited title
Jun
18
comment What happens geometrically when the Jacobson radical is non-zero?
Naturally I do not think there is actually anything wrong with it. I removed the comment on separation; oops. I also tweaked the question, since we're not actually looking at the ring of real-valued functions on an affine scheme. I'm looking for intuition, and phenomena which can be directly attributed to a non-vanishing Jacobson radical $J$. How does for instance the space $Spec(A/J)$ look compared to $Spec(A)$. Hopefully the question is in better shape now. Thanks for the feedback!
Jun
18
revised What happens geometrically when the Jacobson radical is non-zero?
deleted 47 characters in body
Jun
18
comment What happens geometrically when the Jacobson radical is non-zero?
Old habit from writing mails, but I might as well stop if anyone feels it worth commenting on.
Jun
18
asked What happens geometrically when the Jacobson radical is non-zero?
Jun
13
comment etale space v. covering space
So covering map $\Leftrightarrow$ étale map? This is a surprise to me. I think my attempts to locally trivialize an arbitrary étale map rely on tacit assumptions.
Jun
11
comment How to study math to really understand it and have a healthy lifestyle with free time?
I'd try to get an overview of whatever I'm learning first. I'd like to think of it as a big canvas; fill in the details according to whatever piques your interest. You absolutely positively can't learn everything (not even close), but you can learn top-down instead of bottom-up. For your comments on rigour, you might find this interesting: cheng.staff.shef.ac.uk/morality/morality.pdf
May
28
asked What is the universal property of the tangent bundle of a smooth manifold?
May
25
comment Is there a universal property of $\text{Spec}(-)$?
Exactly; thank you!
May
25
accepted Is there a universal property of $\text{Spec}(-)$?
May
25
comment Is there a universal property of $\text{Spec}(-)$?
I clarified this assumption in the OP.
May
25
revised Is there a universal property of $\text{Spec}(-)$?
added 34 characters in body
May
25
comment Is there a universal property of $\text{Spec}(-)$?
I knew about that, but I'm thinking about $\text{Spec}$ as a functor $\text{Ring}^{op}\to\text{LRSpaces}$. This question may still be silly though :)
May
25
asked Is there a universal property of $\text{Spec}(-)$?
May
19
answered Soft Question - Intuition of the meaning of homology groups
May
7
revised Is there a noetherification of locally noetherian schemes?
deleted 111 characters in body
May
4
revised Is there a noetherification of locally noetherian schemes?
deleted 48 characters in body; edited body
May
4
asked Is there a noetherification of locally noetherian schemes?
Apr
28
comment Natural Isomorphism $\mbox{Hom}(\oplus_\alpha A_\alpha,G) \simeq \prod_\alpha \mbox{Hom}(A_\alpha,G)$
@Qwirk: That's precicely what happens in this case as well, but with different words in it. By definition, a morphism from the coproduct is the same thing as a morphism from each of its factors.