H. Hasson
  • Member for 12 years, 1 month
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  • Palo Alto, CA
tamely branched cover over P^1
Accepted answer
9 votes

Here's an alternative way to think about it: You can easily deduce from Riemann-Hurwitz that the genus of X is 0, i.e. it is just the projective line. Look at the affine patch: t is not infinity. ...

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Branched coverings of Riemann surfaces with specified branch points.
6 votes

Yes. The fundamental group of this Riemann surface minus those branch points is $< a_1, b_1, ..., a_g, b_g, c_1, ..., c_r| [a_1,b_1]...[a_g,b_g]c_1...c_r=1>$ (where $g$ is the genus, and $r$ is ...

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Etale covers of the affine line
6 votes

I see that this question is from a while back, but I figured I add this little morsel: Manish Kumar proved for his thesis that the commutator subgroup of the algebraic fundamental group of A^1 (and, ...

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Why certain diophantine equations are interesting (and others are not) ?
3 votes

This certainly isn't something I thought a lot about, but there has definitely been interest about "Generalized Fermat Equations" (like the one you listed). Here's a quick link that I found googling ...

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Deformations of Tame Coverings
Accepted answer
3 votes

A paper I'm reading now is a PERFECT reference for this: "Deformation of tame admissible covers of curves" by Stefan Wewers is written in an expository style. (corollary 3.1.3 is exactly the theorem ...

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Two questions on isomorphic elliptic curves
3 votes

Hopefully I'll have some time later to ellaborate, but for now - here is a great reference I wish somebody had shown me when I started out, for how to attack questions of this type: http://books....

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When two k-varieties with the same underlying topological spaces isomorphic?
3 votes

Here is a possible statement: If f:X->Y and g:X->Y are two finite morphisms of schemes that agree topologically, and they give the same homomorphisms on all the residue fields (if x goes to y, f and ...

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Surprising Analogue of Q
2 votes

Alright, I think I should write my 2 cents here: Obviously $Spec(\mathbb{Q})$ and $\mathbb{A}_K$ are not directly analogous, but they do appear to be in relation to this problem. It seems that they ...

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Sylow Subgroups
2 votes

I don't know if this was the original motivation, but this has some interesting motivating ideas: Abstract nonsense versions of "combinatorial" group theory questions

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Does the axiom of specification prevent writing any proof?
1 votes

It's been a good five years or so since I've done logic, so this is only a rough sketch: The unintuitive point in formalizing proofs is that ᵩ(t), where t is a variable (what you call a "term"),...

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A problem in algebraic number theory, norm of ideals
1 votes

Hmm... I can see offhand how to deal with it if L/K is Galois, but I'd have to think about it otherwise... In the Galois case, above p you have r many prime ideals, each with ramification index e, and ...

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