# Tagged Questions

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### quasicompact scheme are finite union of affine scheme

This is a problem from Liu`s book. Show that a scheme $X$ is quasi-compact if and only if it is a finite union of affine schemes. If the scheme is quasicompact then it is obviously a finite union of ...
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### Connected scheme but not quasicompact

I am searching for a connected scheme which is not quasi compact. My try: Suppose $A_i$=Spec$k[x]$, where $k$ is algebraically closed field are affine schmes . I am planning to glue $0$ of the ...
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### A doubt in affine schemes

Consider the affine scheme (Spec($A$),$O_{Spec(A)}$). where $A$ is a commutative ring. Then I know (from hartshrone page 71) that $\Gamma (Spec(A),$ $O_{Spec(A)}$) is isomorphic to $A$ . I also know ...
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### Why is Weil restriction right adjoint to base change?

Let $k'/k$ be a finite field extension, and let $X'$ be an affine group scheme over $k'$. We can define the Weil restriction of $X'$ to be the affine group scheme $\mathrm{Res}_{k'/k}(X')$ over $k$ ...
Motivation Let $F$ and $K$ be distinct algebraically closed fields. Then $GL_n(F)$ acts on $M_n(F)$ by conjugation, and the nilpotent orbits of this action can be characterized by the Jordan normal ...