3
votes
0answers
56 views

on Neron defect of smoothness for groups schemes

Let $G$ a semisimple simply connected group over $\mathbb{C}$. Let $\gamma\in G(\mathbb{C}[[t]])$ such that $\gamma$ is regular semisimple on $G(\mathbb{C}((t)))$. We consider $I_{\gamma}$ the group ...
2
votes
0answers
64 views

semicontinuity of the conductor defined by Temkin

We say a principal pair $(X,\mathcal{I})$ where $X=Spec(A)$ is affine scheme and $\mathcal{I}=\tilde{I}$ where $I\subset A$ is a principal ideal generated by $\pi$ wich is a non zero divisor. For a ...
5
votes
0answers
276 views

What is known about “singularity types” in the Murphy's Law sense?

In his "Murphy's Law" paper, Vakil gives a definition equivalent to the following: The singularity type of a pointed scheme $(X,p)$ its equivalence class, under the following equivalence relation: ...
4
votes
1answer
464 views

When singular points of a reduced scheme are not dense in it?

A stupid AG question: could singular (Zarisky) points be dense in a reduced (Noetherian) scheme $S$? If yes, which 'standard' restrictions on $S$ could ensure that this does not happen? For example, ...