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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

4
votes
1answer
I'm trying to read chapter XIII of SGA1, and I'd appreciate some help about a few issues I'm having. Definition 2.1.1. is of tamely ramified sheaves. The definition is as such: if $U$ is an open sub …
asked Apr 27 '10 by H. Hasson
7
votes
1answer
For any finite group, G, we can find a cover of ℙ1ℂ which is G-Galois. The regular inverse Galois problem is equivalent to there existing such a cover that descends with action to ℚ. My question is ab …
asked Feb 25 '10 by H. Hasson
17
votes
1answer
The question is: for any finite group, $G$, and any finite set of primes (of $\mathbb{Z}$), $P$, is there a number field $K$, such that there is a regular $G$-Galois extension of $\mathbb{P}^1_K$, and …
asked Apr 14 '10 by H. Hasson
18
votes
1answer
Excuse me for the specificity of this question, but this is a silly computation that's been giving me trouble for some time. I want to explicitly realize the order 21 Frobenius group over ℂ(x), as ℂ( …
asked Jan 3 '10 by H. Hasson
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 s …
answered Mar 27 '10 by H. Hasson
4
votes
2answers
Question Say we have a map, C->D, of relative curves over a Dedekind scheme, S. What are some of the available methods for showing that this map has good reduction, or integral reduction, at some s∈S …
asked Jan 15 '10 by H. Hasson
12
votes
2answers
Notation The term "field of moduli" comes in up in different scenarios, but let's consider the following: Let X->ℙ1 be a G-Galois cover, where everything is over the algebraic closure of some field L. …
asked Jan 23 '10 by H. Hasson
1
vote
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 …
answered Dec 18 '09 by H. Hasson
20
votes
5answers
The question is, loosely put, what is known about wild ramification? Is there a semi-well-established theory of wild ramification that can be furthered in various specific situations? Or maybe there …
asked Feb 1 '10 by H. Hasson
5
votes
1answer
Question Let X be a smooth, projective curve over the algebraic closure of ℚ. Let f:X->ℙ1 be a meromorphic function. Assume that the zeros and the poles are defined over some number field, K. Then do …
asked Jan 5 '10 by H. Hasson
21
votes
3answers
I was describing Manish Kumar's work a few weeks ago to a fellow graduate student, and she stumped me with a big-picture question I couldn't answer. Manish Kumar proved that the commutator subgroup o …
asked Apr 1 '10 by H. Hasson
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 a …
answered Apr 8 '10 by H. Hasson
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 i …
answered Oct 16 '10 by H. Hasson