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seen May 17 '13 at 19:44

I will usually wait a few days before accepting an answer.


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awarded  Popular Question
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24
awarded  Autobiographer
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awarded  Enlightened
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awarded  Nice Answer
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awarded  Nice Question
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awarded  Yearling
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comment Curious about Hilbert-Zariski theorem involving homogeneous variety and set of zeroes.
@GeorgesElencwajg Would you be willing to include a citation for where this result appears in EGA?
Mar
7
accepted Deducing results in linear algebra from results in commutative algebra
Mar
7
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
GitGud As written in your Edit1, you can only say that a sub-extension of degree 3 is isomorphic to $\mathbb{Q}(\sqrt[3]{2})$ if you already know that it's generated by a root of $X^3-2$, i.e. assuming what it is we were aiming to show.
Mar
7
accepted Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Mar
4
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Anyway, the case of $[K:\mathbb{Q}]=3$ goes similarly; if $K$ contains a root of $X^3-2$ then we know what $K$ is, but if not then $[K(\sqrt[3]{3}):K]=3$, which is impossible.
Mar
4
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
I don't quite see why your Edit is correct: is it really the case that every extension of degree $3$ is isomorphic to $\mathbb{Q}(\sqrt[3]{2})$? This can't be.
Mar
3
comment If $g$ is an element in an abelian group $G$ and $H\leqslant G$, must there exist an $n$ such that $g^n\in H$?
No. Consider $G = \mathbb{C}^\times$ and $H=\{1\}$. Consider any element $g\in \mathbb{C}$ such that $|g|=1$ but $g$ is not a root of unity. Note that such an element must exist for cardinal reasons.
Feb
21
comment American undergraduate applying overseas
You might be interested in this program as well as another option, or you could apply directly to any number of masters programs at various European universities. Usually a masters is required for PhD enrollment I think, but why not try asking people in the departments you're interested in working in to see what they recommend?
Feb
10
asked Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Dec
24
comment étale fundamental group as unification of galois theory and covering theory
@GeorgesElencwajg After a long enough time, none of us will be remembered. :)
Oct
4
awarded  Quorum