1,490 reputation
918
bio website perso.univ-rennes1.fr/…
location Rennes
age 39
visits member for 5 years, 3 months
seen 28 mins ago

1d
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
comment 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
comment 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With all due respect to the Stacks Project, it is not peer-reviewed...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
comment 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
comment 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 $Y$.
Feb
18
comment $R^{\dim X-\dim Y}f_{\ast}\omega_X \simeq \omega_Y$ in positive characteristic?
Isn't such vanishing the result of Chatzistamatiou and Rülling in "Higher direct images of the structure sheaf in positive characteristic", ANT 2011?