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14h
comment Give me your opinion about those books
Tignol's book is very good, not difficult and definitely worth reading, or at least browsing. It contains material that you will not find in any other book and is written by a world expert in Galois theory.
1d
comment When is tensor product isomorphic to product?
That $ab=ba$ also makes no sense.
2d
comment Krull dimension on localization
@user26857: Grothendieck's revolution consisted in introducing rings with nilpotent elements, which finally allowed to have a definitive theory of Picard schemes, moduli theory, etc... So assuming that rings are domains is excluded in the foundations of scheme theory, whereas noetherianness is a very weak condition, essentially taken for granted in books on the subject: "...we will normally not mention coherent sheaves unless the scheme is noetherian." (Hartshorne, page 111). As to your non-noetherian valuation rings, I challenge you to find ONE mention of them in the 1500 pages of EGA!
2d
comment Krull dimension on localization
@user26857: a) "La critique est aisée, et l'art est difficile" (Destouches, "Le Glorieux"). b) "La critique est un impôt que l’envie perçoit sur le mérite.” (Duc de Lévis)
2d
answered Krull dimension on localization
Apr
27
revised Under which additional hypothesis are open maps locally injective
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Apr
27
comment Under which additional hypothesis are open maps locally injective
Thanks for the kind words Oliver. To answer your second comment: no, I don't know a reasonable condition. As a caveat, beware that the projection $X\times Y\to X$ of a product of topological spaces onto a factor is always open and practically never a local homeomorphism. Similarly a submersion $X\to Y$ of differential manifolds is always open but never a local homeomorphism if $\dim X\gt \dim Y$ ,
Apr
27
revised Under which additional hypothesis are open maps locally injective
added 150 characters in body
Apr
27
revised Under which additional hypothesis are open maps locally injective
added 150 characters in body
Apr
27
answered Under which additional hypothesis are open maps locally injective
Apr
25
comment Show that a polynomial is still irreducible in a extension field
Professor Papantonopoulou, that's Greek to me.
Apr
24
comment Fibers of extension of scalars to algebraic closure of an affine variety is of dimension 0.
@Hoot: ... except for the empty fibers of dimension $-\infty$ .
Apr
24
comment Fibers of extension of scalars to algebraic closure of an affine variety is of dimension 0.
Dear @user26857, because I'm not sure what the OP knows. For example, I don't know the terminology Krull-Cohen-Seidenberg since I learned commutative algebra from Atiyah-Macdonald :-) (and I haven't even read it through yet !)
Apr
24
revised Fibers of extension of scalars to algebraic closure of an affine variety is of dimension 0.
added 421 characters in body
Apr
24
answered Fibers of extension of scalars to algebraic closure of an affine variety is of dimension 0.
Apr
23
comment Tensor product of invertible sheaves
This does not make sense unless you explain what the restriction maps are.
Apr
22
revised Hilbert function and homogenous polynomials.
added 5 characters in body
Apr
22
revised Hilbert function and homogenous polynomials.
added 474 characters in body
Apr
22
comment What exactly is the $O_X$-module and the corresponding sheaf of modules?
I did not downvote you and, yes, you are perfectly entitled to ask your question here. The sheaf $F$ consists of the collection of all $(U,F(U))$'s (just like a function consists of all pairs $(x,f(x))$) plus lots of maps $F(U)\to F(V)$ between those. I can't explain all this any better, so you will have to hope for explanations from another participant and/or read Tennison or some other text. Good luck!
Apr
22
comment Extensions of the quadratic closure of $\mathbb{Q}$
Show that $T^3-2$ has no root in $\mathbb Q^q$, since every element of $\mathbb Q^q$ has degree over $\mathbb Q$ a power of $2$.