Theorem 7.48. (Scholze–Stefanich)
Let \(A\) be a Stefanich ring and let \(n\geq 0\). The opposite of the category \(\StRing^{n\text{-}\et}_{A/}\) of \(n\)-étale Stefanich \(A\)-algebras is a countable topos. More precisely,
\[\Ind_{\aleph_1}\!\left(\bigl(\StRing^{n\text{-}\et}_{A/}\bigr)\catop\right)\]
is a topos.
Proof
This is [Scholze 2026, Theorem 7.1].
References
- Peter Scholze. Geometry and Higher Category Theory. 2026.