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1d
revised Residue fields of schemes of finite type (over $\mathbb{Z}$)
Corrected statement about residue fields and rational points
1d
comment Residue fields of schemes of finite type (over $\mathbb{Z}$)
@Joachim You are right. The correct statement is that, if $X$ is a scheme and $x$ is a closed point, then $x$ is a $k(x)$-rational point. Moreover, if $x$ is a $k$-rational point, then the residue field of $x$ is a subfield of $k$.
Feb
10
comment On algebraic groups of dimension 1
As it is one-dimensional, it will be $(K,+)$ or $(K*, \times)$ or an elliptic curve. You can't get an elliptic curve, because a subvariety of the affine variety $(K,+)^n$ is not projective. So you just have to exclude that you get $K*$. But how would this be a subgroup?
Feb
9
comment Definition of schematically dense
Your affine $k$-scheme $X$ is not a scheme. It is only the set of closed points of the scheme $\mathbb A^1_k$.
Feb
9
comment Residue fields of schemes of finite type (over $\mathbb{Z}$)
@Joachim If X is a scheme and $x$ is a closed point, then $x$ is a $k(x)$-rational point of $X$. Here $k(x)$ is the residue field of $X$.
Feb
7
awarded  Yearling
Jan
27
comment Residue fields of schemes of finite type (over $\mathbb{Z}$)
@Lukas I corrected the proof, as it was incomplete before. I was not using the finite generation of $A$ before which is crucial of course. (If you want to see how finite type is used, consider $Spec \mathbb Q$ as a scheme over $\mathbb Z$.)
Jan
27
revised Residue fields of schemes of finite type (over $\mathbb{Z}$)
Corrected proof of why $m_x\cap \mathbb Z$ is non-zero
Jan
26
answered Residue fields of schemes of finite type (over $\mathbb{Z}$)
Jan
26
awarded  Autobiographer
May
29
comment Automorphisms of manifold vs automorphisms of Hodge structure
@quinque Thank you for your comment. I think the period domain is 15-dimensional (as the intermediate Jacobian is 5-dimensional); see p. 11 of math.ens.fr/~debarre/Periods-MSRInotes2.pdf
May
29
comment Automorphisms of manifold vs automorphisms of Hodge structure
@quinque I'm not sure if there are automorphisms (besides -1) of the intermediate Jacobian of a cubic threefold which don't come from the cubic threefold itself. Do you think that for a cubic threefold $X$, we have $Aut(X) x \{\pm id\} = Aut(J_X)$?
May
29
revised Automorphisms of manifold vs automorphisms of Hodge structure
deleted 56 characters in body
May
28
revised Automorphisms of manifold vs automorphisms of Hodge structure
deleted 334 characters in body
May
28
comment Automorphisms of manifold vs automorphisms of Hodge structure
@quinque you're right. Let me edit my answer.
May
27
awarded  Organizer
May
27
revised Automorphisms of manifold vs automorphisms of Hodge structure
Added some tags
May
27
suggested approved edit on Automorphisms of manifold vs automorphisms of Hodge structure
May
27
answered Automorphisms of manifold vs automorphisms of Hodge structure
May
18
comment Some questions about reduction of elliptic curves
Seems like you're asking about the reduction of $X_0(n)$. Have a look at Katz-Mazur's book Arithmetic moduli of elliptic curves and Brian Conrad's article in J. inst. Jussieu with a similar title.