Abstract
We prove that, for a smooth complete variety X over a perfect field, H i ( X , Z p ( r ) ) ≅ Hom D c b ( R ) ( 1 , R Γ ( W Ω X • ) ( r ) [ i ] ) , where H i ( X , Z p ( r ) ) = lim ← n H i - r ( X et , ν n ( r ) ) (Amer. J. Math. 108 (2) (1986) 297–360), W Ω X • is the de Rham–Witt complex on X (Ann. Scient. Ec. Num. Sup. 12 (1979b) 501–661), and D c b ( R ) is the triangulated category of coherent complexes over the Raynaud ring (Inst. Hautes. Etuder Sci. Publ. Math. 57 (1983) 73–212).
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