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Questions tagged [zariski-topology]

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On the prime spectrum of $R[[X]]$ when the prime spectrum of $R$ is Noetherian

All rings below are commutative with unity. If $R$ has a.c.c. on radical ideals i.e. if $Spec R$ is Noetherian under Zariski topology, then so is $R[X]$, this is Theorem 2.5 in the following paper ...
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A relation between $Spec((1+I)^{-1}R)$ and $Spec(R/J)$

Let $R$ be a commutative ring with identity and let $I$ and $J$ be two finitely generated ideals of $R$. Clearly $1+I:=\{1+i:i\in I\}$ is a multiplicative closed subset of $R$. We can consider the ...
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Bézout and products in algebraic groups

Let $G$ be a linear algebraic group -- be it a Lie group or a group of Lie type. Let $V$, $W$ be subvarieties of $G$. Of course, $V\cap W$ is also a variety (not necessarily irreducible) and $V\cdot W^...
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Convergent sequences in projective varieties

It's very well known that if $X$ is an irreducible projective variety (feel free to assume that the base-field is $\mathbb{C}$), then any two points $x,y\in X$ can be connected by the image of a non-...