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Sep
7
revised Philosophy behind Mochizuki's work on the ABC conjecture
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Sep
7
comment Philosophy behind Mochizuki's work on the ABC conjecture
@quid: the expositions I've seen (such as kurims.kyoto-u.ac.jp/~motizuki/2010-10-abstract.pdf) are mostly teasers to make people read more. My question is about the sketch underlying the proof of the ABC conjecture, which I don't see evident there. If you have an exposition that you would recommend, I suggest that you write it as an answer.
Sep
7
comment Philosophy behind Mochizuki's work on the ABC conjecture
Correction: "an enthusiastic report". Sorry, Jordan!
Sep
7
asked Philosophy behind Mochizuki's work on the ABC conjecture
Aug
29
awarded  Popular Question
Jul
6
awarded  Popular Question
Jul
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awarded  Popular Question
May
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awarded  Nice Question
May
16
comment What is the intuition for $\mathbb{Q}^{ab}$ having cohomological dimension $1$?
Carnahan: can you expatiate a little more about your comment?
May
16
comment What is the intuition for $\mathbb{Q}^{ab}$ having cohomological dimension $1$?
Alex: $\mathbb{Q}^{ab}$ is indeed the maximal abelian extension of $\mathbb{Q}$, but its absolute Galois group is $Gal(\bar{\mathbb{Q}}/\mathbb{Q}^{ab})$ not $Gal(\mathbb{Q}^{ab}/\mathbb{Q})$.
May
15
asked What is the intuition for $\mathbb{Q}^{ab}$ having cohomological dimension $1$?
May
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awarded  Yearling
Mar
10
awarded  Popular Question
Feb
12
accepted Are there n polynomials for which all intersection multiplicities are at least m?
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
Yes, you're right!
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
@Florian: $0$ and $(x-1)^2(x+1)$ intersect with multiplicity $1$ at $x=-1$.
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
Look at the discussion above -- what you suggest will only make the condition hold at $x=a$, but not for other values of $x$. For example try multiplying $0,x,1,x+1$ (which satisfy the condition over $x=0$) by $(x-3)^2$ and see that there are values where some of these intersect with multiplicity $1$.
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
@Will: I want that all of its nonzero roots will have multiplicity $\geq m$. Furthermore, I want that for every $i$ there will exist a unique $j$ such that $0$ is a root of $f_i-f_j$.
Feb
12
revised Are there n polynomials for which all intersection multiplicities are at least m?
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Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
You're right! So I guess this proves the $m=2$, $n=4$ case. I can't see how this would generalize, though...