Books & notes

Higher Topos Theory Section 6.5: Dimension theory

Krull dimension bounds sheaf topos dimension

Example 6.74.

Let \(X\) be a spectral space of Krull dimension \(\leq d\). Then \(\Shv(X)\) has dimension \(\leq d\); see [Clausen and Mathew 2021, Theorem 3.12].

References

  1. Dustin Clausen, Akhil Mathew. Hyperdescent and étale $K$-theory. Invent. Math., 225 (3), 981–1076. 2021.