RIEMANN-HILBERT CORRESPONDENCE FOR UNIT F-CRYSTALS ON EMBEDDABLE ALGEBRAIC VARIETIES

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 etale sheaves of Z/p(n)Z-modules with finite Tor-dimension. We also discuss the relationship of t-structures on these derived categories when n = 1.