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Let $f\colon X\to \mathbb{A}^n_{\mathbb{C}}$ be a flat morphism of $\mathbb{C}$-schemes. Suppose $f$ is (a) separated, (b) flat, (c) locally of finite type, (d) all fibers are quasi-compact, is $X$ necessarily quasi-compact?

Let $f\colon X\to \mathbb{A}^n_{\mathbb{C}}$ be a flat morphism of $\mathbb{C}$-schemes. Suppose $f$ is (a) separated, (b) flat, (c) locally of finite type, (d) all fibers are quasi-compact, is $X$ necessarily quasi-compact?

Let $f\colon X\to \mathbb{A}^n_{\mathbb{C}}$ be a morphism of $\mathbb{C}$-schemes. Suppose $f$ is (a) separated, (b) flat, (c) locally of finite type, (d) all fibers are quasi-compact, is $X$ necessarily quasi-compact?

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fiberwise-quasi-compact implies quasi-compact?

Let $f\colon X\to \mathbb{A}^n_{\mathbb{C}}$ be a flat morphism of $\mathbb{C}$-schemes. Suppose $f$ is (a) separated, (b) flat, (c) locally of finite type, (d) all fibers are quasi-compact, is $X$ necessarily quasi-compact?