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seen Mar 26 at 11:04

Mar
1
revised Factorization of primes and $Spec(\mathcal{O}_K)$
edited body
Mar
1
answered Factorization of primes and $Spec(\mathcal{O}_K)$
Feb
11
comment determinant inequality
@user6910 No problem. Now that you added your geometric motivation at least who answers has less the impression of wasting his time. In the counterexamples given by Arturo and me the parallelograms are not degenerate, but in any case you shouldn't be afraid of considering degenerate cases! You could try to see them as limits of non-degenerate cases.
Feb
11
comment determinant inequality
@user6910 Could you please stop changing the question? I edited the answer to give you another counterexample, but please try at least to think about the problem yourself before posting it here.
Feb
11
awarded  Editor
Feb
11
revised determinant inequality
added 20 characters in body; edited body
Feb
11
awarded  Commentator
Feb
11
comment determinant inequality
Then $(a,b)=(3,1)$, $(c,d)=(0,1)$, $(e,f)=(1,0)$ is again a counterexample. Maybe the condition is another one?
Feb
11
answered determinant inequality
Feb
10
comment Symbols for Quantifiers Other Than $\forall$ and $\exists$
I've sometimes seen $\forall\forall$ used to mean "for all but finitely many elements", but I don't know if this is a common convention or not.
Feb
10
comment Morphisms of finite type are stable under base change
You're welcome!
Feb
10
answered Morphisms of finite type are stable under base change
Feb
10
comment Morphisms of finite type are stable under base change
The first claim of your second paragraph is true: if $f:X\to Y$ is a morphism of schemes and $V\subset Y$ then $f^{-1}(V)\cong X\times_Y V$; you can easily see that $f^{-1}(V)$ satisfies the universal property of the fibered product. Your statement follows then from the properties of the fibered product.
Feb
10
comment When to learn category theory?
I don't know if it should be considered "elementary category theory", but the fact that a functor is an equivalence of categories if and only if it is fully faithful and essentially surjective is an higly nontrivial result in my opinion.
Feb
10
comment When to learn category theory?
Well, of course you can read what categories and functors are (I'm pretty sure that the OP already did), but the only point that I can see for doing this is to recognise a functor as you see one (which imo is a good thing precisely because you prepare yourself for when you'll really learn category thoery). I'd say that there's no need at all of more advanced category theory before you'll actually need to use tools like equivalences of categories or limits.
Feb
9
awarded  Teacher
Feb
9
comment When to learn category theory?
(I actually wanted to write my small anecdote as a comment but it looks like I don't have enough reputation to comment on other people's posts)
Feb
9
answered When to learn category theory?
Jan
28
awarded  Scholar
Jan
28
comment Is every finite separable extension of a strictly henselian DVR totally ramified?
Oh, I just realized that moreover if $K$ has characteristic 0 then you can take $\sigma=0$ in your argument, and if $K$ contains the $p$-th roots of unity then the extension $L|K$ is also Galois, wow. (But I have no idea whether this can be easily achieved also in the same char case)