A Riemann-Hilbert correspondence for Cartier crystals

2018/12/01 by Schedlmeier, Tobias
#13A35 (Secondary) #14G17 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.00256

Abstract

For a variety X separated over a perfect field of characteristic p>0 which admits an embedding into a smooth variety, we establish an anti-equivalence between the bounded derived categories of Cartier crystals on X and constructible \mathbb Z/p \mathbb Z-sheaves on the étale site X_ét. The key intermediate step is to extend the category of locally finitely generated unit \mathcal O_F,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 D_c^b(X_ét,\mathbb Z/p \mathbb Z).

Related

• Cartier crystals and perverse constructible étale p-torsion sheaves
• Riemann-Hilbert correspondence for unit F-crystals on embeddable algebraic varieties
• Duality between Cartier crystals and perverse \mathbbF_p-sheaves, and application to generic vanishing
• Intermediate extensions of perverse constructible \mathbbF_p-sheaves commute with smooth pullbacks
• Cartier Crystals