913 reputation
511
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location Oslo, Norway
age 26
visits member for 4 years, 1 month
seen Sep 18 at 12:51

Master student in algebraic topology at the University of Oslo.


May
26
comment Combinatorics of the Zeta function of a variety
'May be' of course, not 'is' :-)
May
26
comment Combinatorics of the Zeta function of a variety
Qiaochu: I think what hilbert points out is that a closed point is of codimension $>1$.
Nov
22
comment Intuition behind Matrix Multiplication
@lhf When you extend multiplication to fractions or the real line like you do, I'm sure you agree that the intuitive 'counting' operation of multiplying integers extends to the intuitive operation of 'scaling'.
May
31
comment Prove $\mathbb{Z}$ is not a vector space over a field
Nice solution! Getting rid of the simplest (characteristic $2$) case as neatly as possible, and then using this directly to support the initial intuition: "fields have fractions." Om nom chomp.
May
2
comment Why is one “$\infty$” number enough for complex numbers?
I see your point of view as well; there are apparently many angles on a somewhat open question. My approach was to point out that the dichotomy between the case of $\mathbb{R}$ and $\mathbb{C}$ implied by the word 'instead' could be considered somewhat artificial o_O
Apr
14
comment Which functor does the projective space represent?
This got way clearer with time. Thanks again :-)
Apr
14
comment Which functor does the projective space represent?
Ah, the condition that the $r_i$ generate $R$ got much clearer when considering that this means that they do not all vanish at any point. This plugs nicely into thinking about projective schemes as looking for strictly non-trivial solutions to homogeneous equations. Neat :-)
Mar
17
comment Which functor does the projective space represent?
Thank you! Another good answer. Hard to know which one to pick, but I think I'll go for this one because it is closer to the generality I asked for. I also found this treated in a set of notes by Strickland on formal schemes.
Mar
16
comment Which functor does the projective space represent?
Thank you! I agree charts might not be all too great for understanding projective spaces, but the first thing I really understood and liked was the projective line, patched together by pieces of $k[t]$. It makes it clear to me why a meromorphic function on $X$ is the same thing as a morphism $X\to\mathbb{P}^1$. This complements nicely the notion of a regular function as a morphism $X\to\mathbb{A}^1$. If I was able to see from the definition of $\mathbb{P}^I$, that this was the case I would be every happy. At least you've told me what I need to stare at until it makes sense :-)
Nov
20
comment cup products and smash products
Ok, I have no Idea what this question is actually asking anymore, but I'm glad you managed to find a satisfactory answer for yourself.
Oct
14
comment What's $F'(x)$ if $F(x) = \int_a^{g(x)} H(x,t) dt$?
This is probably the favourite answer I've read on Stackexchange yet :-) So unbelievably natural, thank you!
Aug
19
comment Why is one “$\infty$” number enough for complex numbers?
I'd love it if that downvote came with a comment.
Aug
10
comment False proof of $H_0 ( X) = 0$
That's it, Matt :-)
Jul
18
comment intersection of two affine open sets of a scheme
Is the union of the $U,V$ off the mark here? A lower bound would be the open set. Am I missing something?
Jul
5
comment What happens geometrically when the Jacobson radical is non-zero?
Well I think that answers my question pretty well to be honest. So thanks!
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
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
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
25
comment Is there a universal property of $\text{Spec}(-)$?
Exactly; thank you!