Example 6.75.
If \(X\) is a qcqs scheme, then the following bounds hold:
\(\dim(X_{\mathrm{Nis}}) \leq \dim_{\mathrm{Krull}}(X)\); see [Clausen and Mathew 2021, Theorem 3.18].
\(\dim(X_{\mathrm{cdh}}) \leq \dim_{\mathrm{val}}(X)\); see [Elmanto et al. 2021, Theorem 2.4.15].
References
- Dustin Clausen, Akhil Mathew. Hyperdescent and étale $K$-theory. Invent. Math., 225 (3), 981–1076. 2021.
- Elden Elmanto, Marc Hoyois, Ryomei Iwasa, Shane Kelly. Cdh descent, cdarc descent, and Milnor excision. Math. Ann., 379 (3--4), 1011–1045. 2021.