2016/03/24 by Tobias Schedlmeier, Schedlmeier, Tobias · 1 citation
Mathematics · #13A35 (Secondary) #14G17 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1603.07696
openalex publication_date 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an F-finite scheme X separated over a perfect field k of characteristic p>0 which admits an embedding into a smooth k-scheme, we establish an equivalence between the bounded derived categories of Cartier crystals on X and constructible ℤ/pℤ-sheaves on the étale site Xét. The key intermediate step is to extend the category of locally finitely generated unit OF,X-modules for smooth schemes introduced by Emerton and Kisin to embeddable schemes. On the one hand, this category is equivalent to Cartier crystals. On the other hand, by using Emerton-Kisin's Riemann-Hilbert correspondence, we show that it is equivalent to Gabber's category of perverse sheaves in Dcb(Xét,ℤ/pℤ). Furthermore, we define intermediate extensions for Cartier crystals and show that our equivalence between Cartier crystals and perverse constructible étale sheaves commutes with the intermediate extension functor.