p-adic Geometry and Homotopy Theory - Département de ...

X lifted to Z smooth /W n ,(a 0 , · · · , a n−1 ) ∈ W n O X↦→ b pn0 + pbpn−1 1 + · · · + p n−1 b p n−1∈ H 0 (X/W n ) = H 0 dR (Z/W n)b i ∈ O Z ↦→ a ii = 1 : W n Ω 1 ∼X −→ σ∗ n H 1 (X/W n ) = σ∗ n HdR 1 (Z/W n)d(a 0 , · · · , a n−1 ) ↦→ ∑ b pn−i−1i db i(cf. Serre’s map F n d : W n O X → Ω 1 X ) 40