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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 $X$).
Mar
19
answered Is the category of schemes wellpowered? regularly wellpowered?
Mar
19
comment Is the category of schemes wellpowered? regularly wellpowered?
But this implies the same property for the category of schemes; in fact this is stated here but I could not find a proof there, so I am giving one in a second answer.
Mar
19
comment Is the category of schemes wellpowered? regularly wellpowered?
Do you have a reference for the wellpoweredness of $\mathbf{Aff}$?
Mar
18
comment Is the category of schemes wellpowered? regularly wellpowered?
The quasicompact (or reduced) assumption is needed to embed $Y$ as an open subscheme of a closed subscheme of $X$. To factor the oher way, there is no condition (and this follows easily from the definition of an immersion).
Mar
18
revised Is the category of schemes wellpowered? regularly wellpowered?
edited body
Mar
18
answered Is the category of schemes wellpowered? regularly wellpowered?
Mar
14
awarded  Nice Answer
Mar
2
awarded  Nice Answer
Feb
13
comment Bertini type theorem
And when $\dim X>1$, the argument shows that $f_{\vert X\cap H}$ is nonconstant for every $H$.
Feb
11
awarded  Good Answer
Jan
26
comment Tensor powers of an algebra all isomorphic
"Which means $A\subset K$": yes assuming e.g. that $k$ is a domain and $A\neq0$. In fact, the zero algebra is a counterexample to many claims. Also, "finitely presented" is irrelevant, I think.
Jan
23
awarded  ag.algebraic-geometry
Jan
22
answered 'Cohomologically approximating' a $\mathbb{Q}[[t]]$-scheme by a one over the henselization of $\mathbb{Q}[t]$?