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Higher Topos Theory Section 7.5: Analytic stacks

Six-functor formalism on analytic rings

Proposition 7.43.

There is a presentable six-functor formalism

\[D\colon \Span(\AnRing\catop, \AnRing^{!,\op}) \to \Pr, \qquad A \mapsto \Mod_A.\]
Proof
The proper and open classes above satisfy the compactification, base-change, and projection-formula hypotheses, and every \(!\)-able map has the factorization of Lemma 7.42. The resulting analytic six-functor formalism is constructed in [Scholze 2025, Lecture IX]. The formal assembly of the coherent span-valued functor may also be expressed using [Cnossen et al. 2025].

References

  1. Peter Scholze. Six-Functor Formalisms. 2025.
  2. Bastiaan Cnossen, Tobias Lenz, Sil Linskens. Universality of span 2-categories and the construction of 6-functor formalisms. 2025.