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Sep
30 |
answered | Scheme of irreducible components |
Aug
25 |
comment |
Reference for the statement that the complement of an affine open has codimension one
EGA IV, part 4 (IHES no 32), Cor. 21.12.7. |
Aug
18 |
comment |
Relationship between $N_{A/K}$ and the reduced norm $\text{nr}_{A/k}$?
Well, not every finite-dimensional algebra is central simple. |
Jun
21 |
answered | meaning of $k$-rational for closed subschemes |
Jun
18 |
accepted | Book on the tetrahedron |
Jun
18 |
comment |
Book on the tetrahedron
Indeed there is a way - I'll buy the book and see. |
Jun
18 |
comment |
Book on the tetrahedron
Seems interesting indeed... |
Jun
18 |
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Book on the tetrahedron
Yes, that's the website of the publisher in Zagreb, Croatia. I sent a mail there to see if there is a way to buy the book. Thanks, |
Jun
18 |
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Book on the tetrahedron
Thank you! These books seem interesting, especially the first. Now comes the question: how can I put my hands on it? It's not in my local library and I can't even seem to find it for sale somewhere on the web... |
Jun
17 |
asked | Book on the tetrahedron |
May
7 |
comment |
When is the Hom-scheme connected?
No, your functor is not representable by a scheme, already e.g. for $A=B=k[X]$. |
May
6 |
awarded | Yearling |
Apr
17 |
comment |
Reference for a lemma on étale maps
With all due respect to the Stacks Project, it is not peer-reviewed... |
Mar
31 |
comment |
When does an algebraic space that is a torsor over a scheme have to be a scheme?
For Q1, a precise reference is SGA1, Exp. VIII, Cor. 7.9. In fact SGA1, Exp. VIII, sec. 7 gives a list of criteria as in your Q3. |
Mar
31 |
comment |
Flatness and intersection of fibers
Certainly not. Geometrically $Y_1=Spec(B_1)$ and $Y_2=Spec(B_2)$ are closed subvarieties in some affine space $\mathbb{A}^{n+1}_X$ with $X=Spec(A)$ and you are asking: is it true that $Y_1,Y_2$ flat over $X$ imply $Y_1\cap Y_2$ flat over $X$? A counterexample is e.g. $X=\mathbb{A}^1_{\mathbb{C}}$ and $Y_1,Y_2=$ the coordinate axes in $\mathbb{A}^2_{\mathbb{C}}$. |
Mar
31 |
comment |
Structure of $\text{Aut}_R(R[X])$
All $R$-automorphisms of $R[X]$ are substitutions $X\mapsto a_0+a_1X+a_2X^2+\dots+a_nX^n$ with $a_i\in R$ and $a_0$ arbitrary, $a_1$ invertible, $a_i$ nilpotent for $i\ge 2$. This is either an exercise, or (I believe) stated somewhere in Demazure-Gabriel. |
Mar
27 |
comment |
How far is it to extend the results of SGA III Exp. VIB from group schemes to group spaces?
You're perfectly right that the assumptions of condition (ii) of sga3 exp.viB Cor.4.4 are met. The point I was worried about is whether (ii) should imply (i) in loc. cit., and it is quite striking that for reduced $S$ (as in your case) this implication holds. Apologies! |
Mar
26 |
comment |
How far is it to extend the results of SGA III Exp. VIB from group schemes to group spaces?
Maybe could you have a look at Lemma 4.2.8 in the paper S. Brochard, Foncteur de Picard d’un champ algébrique, Math. Ann. 2009. Also note that this has been extended to alg. stacks in an Erratum to the paper, available on the author's webpage. |
Mar
26 |
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How far is it to extend the results of SGA III Exp. VIB from group schemes to group spaces?
Dear Heer, do you in fact assume that $G$ is smooth over $S$? If I'm not mistaken, with your assumptions it could be that $G=G_s\amalg G_t$ mapping to $S$ in the natural way, which I doubt you want to consider. |
Feb
25 |
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Implicit Function Theorem on Singular Varieties
Dear Giulio, in Algebraic Geometry the property of finiteness has a specific meaning which implies properness. The example of Laurent is bijective but not proper since the image of the closed subset $X_2$ is not closed in $Y$. |