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13h
comment Proper monomorphisms in complex analytic spaces
@user74230: yes, but a monomorphism is automatically separated.
Nov
22
comment 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
comment 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
comment 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
comment Smoothness and smoothness over formal neighborhood
Please give precise definitions for $X_x$ and $Y_y$.
Nov
11
comment 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
comment 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
comment Reciprocal polynomials with roots off the unit circle
"Irreducible": over what field?
Sep
29
comment 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
comment 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
comment 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
comment preservation of localness among certain Krull domains
I agree with Mathias, but I can't prove anything yet. I suggest you look at the 2-dimensional 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
comment Counterexamples to Elkik's theorem in the non-Noetherian case
$B$ is only smooth over $A[a^{-1}]$.