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1d
comment Counterexamples to Elkik's theorem in the non-Noetherian case
$B$ is only smooth over $A[a^{-1}]$.
1d
comment irreducible etale cover of a blowup
What does the index $i$ mean?
Jul
16
awarded  Yearling
Jul
7
comment R[[X]] flat as a R[X]-module?
If $R[[X]]$ is flat over $R[X]$ then it is flat over $R$. So $R^\mathbb{N}$ must be a flat $R$-module; in other words, $R$ is a coherent ring.
Jul
2
awarded  Curious
Jun
25
comment Completion of Bezout Domain a Bezout Domain?
To start with, it is not necessarily a domain: if you take $R=\mathbb{Z}$ and $I=6\mathbb{Z}$, the completion is $\mathbb{Z}_2\times\mathbb{Z}_3$.
May
27
comment Variant of Hilbert 90 for Galois extensions
@Daniel Loughran: If $g=1$, $\mathrm{Aut}(K)$ is an extension of the finite group of (pointed) automorphisms of an elliptic curve by the group of translations of the same, which is also finite since the ground field is. So, it seems that $\mathrm{Aut}(K)$ is finite in all cases.
May
22
comment Is every element of $\mathrm{SL}(n,R)$ of finite order diagonalizable?
This argument only decomposes the representation as a direct sum of projective submodules on which $G$ acts via a character. These submodules need not be free, so the question is: what does "diagonalizable" mean? For instance, assume there is a nontrivial invertible $R$-module $L$ such that $E:=L\oplus L\cong R^2$. Then the endomorphism of $E$ which is $1$ (resp. $-1$) on the first (resp. second) factor $L$ is not diagonalizable in the naive sense.
May
6
comment A strengthened version of Noether's normalisation lemma?
Clearly not if $\mathrm{Frac}(R)$ is not separable over $k$. Otherwise, I think it's true. I suggest you have a look at Bourbaki.
May
5
answered Constructing a ring whose spectrum is given by order ideals of Z with generic point
May
5
comment Does every reductive group scheme admit a maximal torus?
@Marty: I don't get it . This only works if $T$ is split.
Apr
29
awarded  Enlightened
Apr
29
awarded  Nice Answer
Apr
6
awarded  Nice Answer
Mar
28
comment Relation between dimension of Proj(S) and dimension of S
In the definition of Proj, don't you want $P$ to be graded?
Mar
27
comment Is $G_{\operatorname{red}}$ normal in $G$?
@user76758: in fact, you get exactly my example "in nature" with your construction by taking for $H$ the group of affine automorphisms of the line (except this $H$ is not semisimple).
Mar
27
answered Is $G_{\operatorname{red}}$ normal in $G$?
Mar
20
comment Is the category of schemes wellpowered? regularly wellpowered?
Unfortunately, a morphism of affine schemes which is a regular mono of schemes (i.e. an immersion) is not necessarily a regular mono in $\mathbf{Aff}$ (i.e. a closed immersion).
Mar
20
awarded  Nice Answer
Mar
20
comment Is the category of schemes wellpowered? regularly wellpowered?
You can take $I=\vert Y\vert$ (the underlying space of $Y$, which is smaller than $\vert X\vert$). For each $y\in I$, choose $V_y$ and $U_y$ such that $y\in V_y$. (We don't need the $U$'s to cover $X$).