All Questions

Is there a geometric picture justifying why "stable points" in GIT (Geometric Invariant Theory) are actually called "stable"? Stable, with respect to which effect? (Here, I have ...

Let $G$ be an abstract finite group acting on a separated $k$-scheme $X$. ($k$ a field; note we can canonically promote $G$ to a $k$- scheme). Then a result by Demazure and Grothendieck (in "...

Let $X$ be a scheme locally of finite type over a sufficiently "nice" base scheme $S$ (nice in sense of reasonable "finiteness conditions", for sake of simplicity let's start as ...

Let $X:=\operatorname{Spec}(R)$ an affine Noetherian scheme and $G$ a finite group acting on $X$. Then it is known that the quotient $Y=X/G$ exists as affine scheme $\operatorname{Spec}(R^G)$, let set ...

This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it. Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite ...

I have some questions about GIT quotients and extensions of scalars of categorical quotients: 1) Let $X$ be a complex algebraic quasi-affine variety, $G$ an algebraic reductive group over $\...