Riemann-Hilbert correspondence for unit F-crystals on embeddable algebraic varieties

2016/01/07 by Ohkawa, Sachio
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.01525

Abstract

For a separated scheme X of finite type over a perfect field k of characteristic p>0 which admits an immersion into a proper smooth scheme over the truncated Witt ring W_n, we define the bounded derived category of locally finitely generated unit F-crystals with finite Tor-dimension on X over W_n, independently of the choice of the immersion. Then we prove the anti-equivalence of this category with the bounded derived category of constructible étale sheaves of \mathbb Z/pⁿ\mathbb Z-modules with finite Tor dimension. We also discuss the relationship of t-structures on these derived categories when n=1. Our result is a generalization of the Riemann-Hilbert correspondence for unit F-crystals due to Emerton-Kisin to the case of (possibly singular) embeddable algebraic varieties in characteristic p>0.

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