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location  Rennes, France  
age  63  
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13h

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Proper monomorphisms in complex analytic spaces
@user74230: yes, but a monomorphism is automatically separated. 
Nov 22 
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About the Dimension of a complete local ring
All I prove is that if $n\geq2$ then $\dim A\geq2$. If $\dim A\leq1$, this forces property 2. 
Nov 20 
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Smoothness and smoothness over formal neighborhood
And meanwhile, I have realized that the same example was given by Anton Geraschenko in answer to this question. 
Nov 20 
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Smoothness and smoothness over formal neighborhood
Right. Without this assumption, taking completions (of local rings) may lead to strange things. 
Nov 19 
answered  Smoothness and smoothness over formal neighborhood 
Nov 19 
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Smoothness and smoothness over formal neighborhood
Please give precise definitions for $X_x$ and $Y_y$. 
Nov 11 
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Does every relative curve have a Picard scheme?
Assume $g=1$. If $S$ is normal, then $X=\underline{\mathrm{Pic}}^1_{X/S}$ is locally projective over $S$ by the main theorem in the introduction to Raynaud's thesis (LNM 119, also Corollaire VI.2.5). By the first comment of user52824, it follows that $\underline{\mathrm{Pic}}_{X/S}$ is a scheme (in fact each $\underline{\mathrm{Pic}}^n_{X/S}$ is locally projective over $S$). 
Nov 3 
awarded  Nice Answer 
Nov 1 
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Is a “central” extension of $\mathbb{Z}/m\mathbb{Z}$ by $\mathrm{GL}_n$ necessarily split?
For a simple explicit example, you can take $k=\mathbb{R}$ and $n=1$, and take for $E$ the subgroup of $\mathrm{GL}_2$ generated by the center and the rotation $\begin{pmatrix}0&1\\1&0\end{pmatrix}$. 
Oct 8 
answered  About the Dimension of a complete local ring 
Oct 7 
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Reciprocal polynomials with roots off the unit circle
"Irreducible": over what field? 
Sep 29 
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Classification of rings satisfying $a^4=a$
I think you mean that $T_0$ is the fixed ring of $\alpha$, not $\alpha(R)$ (the latter is $R$ since $\alpha$ is an involution). 
Sep 23 
answered  Non trivial family of hyperelliptic curves 
Sep 20 
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Locally Closed Orbits in Real Algebraic Geometry
Take $G=SL_2$ and $Y=SL_2/(\pm1)=PGL_2$, with $x_0=1$. Then $\Omega=PSL_2(\mathbb{R})=SL_2(\mathbb{R})/(\pm1)$, while $Y(\mathbb{R})$ has another component, containing the class of $\begin{pmatrix}0&i\\ i&0\end{pmatrix}$ (the matrix is not real but its image in $Y$ is). I doubt very much that you can find interesting conditions on $G$ alone (well, "$G$ unipotent" would do, I guess). By the above discussion, the key point is the structure of stabilizers. 
Sep 20 
answered  Locally Closed Orbits in Real Algebraic Geometry 
Sep 18 
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Locally Closed Orbits in Real Algebraic Geometry
@Daniel: I think that the "$G$orbits" here are the orbits of $G(\mathbb{R})$ acting on $X(\mathbb{R})$. 
Sep 17 
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preservation of localness among certain Krull domains
I agree with Mathias, but I can't prove anything yet. I suggest you look at the 2dimensional case. In this case, if you denote by $U$ the complement of the closed point in $\mathrm{Spec}(R)$, then $S$ is the ring of global functions on $V:=U\smallsetminus\{\mathfrak{p}\}$, and I would rephrase Mathias's intuition by saying that $V$ might be affine (in which case, of course, $S$ is not local since $\mathrm{Spec}(S)=V$). 
Sep 6 
revised 
Existence of affine hulls
Added some results (in particular Theorem 1). 
Aug 31 
answered  Existence of affine hulls 
Aug 28 
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Counterexamples to Elkik's theorem in the nonNoetherian case
$B$ is only smooth over $A[a^{1}]$. 