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András Bátkai
András Bátkai
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Let $X$ be the underlying space of a scheme. If $X$ is irreducible of finite Krull dimension, is it necessarily quasi-compact? Is it necessarily Noetherian? What if we assume not only that Krull dimension is finite but also that it is 1?

  • If $X$ is irreducible of finite Krull dimension, is it necessarily quasi-compact?
  • Is it necessarily Noetherian?
  • What if we assume not only that Krull dimension is finite but also that it is 1?

Let $X$ be the underlying space of a scheme. If $X$ is irreducible of finite Krull dimension, is it necessarily quasi-compact? Is it necessarily Noetherian? What if we assume not only that Krull dimension is finite but also that it is 1?

Let $X$ be the underlying space of a scheme.

  • If $X$ is irreducible of finite Krull dimension, is it necessarily quasi-compact?
  • Is it necessarily Noetherian?
  • What if we assume not only that Krull dimension is finite but also that it is 1?
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schematic_ftm
schematic_ftm
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Irreducible of finite Krull dimension implies quasi-compact?

Let $X$ be the underlying space of a scheme. If $X$ is irreducible of finite Krull dimension, is it necessarily quasi-compact? Is it necessarily Noetherian? What if we assume not only that Krull dimension is finite but also that it is 1?