Year: 2025
Type: article
Abstract: We construct a derived stack $$\mathcal {X}$$ X of Laurent F-crystals on "Equation missing", where $$\mathcal {O}_K$$ O K is the ring of integers of a finite extension K of $$\mathbb {Q}_p$$ Q p . We first show that its underlying classical stack $$^\textrm{cl}\mathcal {X}$$ cl X coincides with the Emerton–Gee stack $$\mathcal {X}_\textrm{EG}$$ X EG , i.e. the moduli stack of étale $$(\varphi ,\Gamma )$$ ( φ , Γ ) -modules. Then we prove that the derived stack $$\mathcal {X}$$ X is classical in the sense that when restricted to truncated animated rings, $$\mathcal {X}$$ X is equivalent to the sheafification of the left Kan extension of $$\mathcal {X}_\textrm{EG}$$ X EG along the inclusion from the classical commutative rings to animated rings.
Source: Mathematische Annalen
Author: Yu Min
Institution: Imperial College London
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4413378477