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I had fix some mistake
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edit approved Jun 6, 2018 at 11:21
Armando j18eos
edit approved Jun 6, 2018 at 11:21
Armando j18eos
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Is it true that any etaleétale morphism is quasi-affine?

Let $\phi:X\to Y$ be an etaleétale morphism of noetherian schemeNoetherian schemes. Does $\phi$ have to be quasi-affine? In other wardswords, if $Y$ is affine does it mean that $X$ is quasi-affine?

It will follow from the fact that quasi-finitfinite morphisms are quasi-affine, but I do not know whether this is true.

Is it true that any etale morphism is quasi-affine?

Let $\phi:X\to Y$ be an etale morphism of noetherian scheme. Does $\phi$ have to be quasi-affine? In other wards, if $Y$ is affine does it mean that $X$ is quasi-affine?

It will follow from the fact that quasi-finit morphisms are quasi-affine, but I do not know whether this is true.

Is it true that any étale morphism is quasi-affine?

Let $\phi:X\to Y$ be an étale morphism of Noetherian schemes. Does $\phi$ have to be quasi-affine? In other words, if $Y$ is affine does it mean that $X$ is quasi-affine?

It will follow from the fact that quasi-finite morphisms are quasi-affine, but I do not know whether this is true.

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Rami
Rami
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Is it true that any etale morphism is quasi-affine?

Let $\phi:X\to Y$ be an etale morphism of noetherian scheme. Does $\phi$ have to be quasi-affine? In other wards, if $Y$ is affine does it mean that $X$ is quasi-affine?

It will follow from the fact that quasi-finit morphisms are quasi-affine, but I do not know whether this is true.