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

• case X/S smooth : Berthelot-Ogus isomorphismK ⊗ W H m (Y/W )∼ −→ H m dR (X K/K)⇒ (K 0 , ϕ)-structure (N = 0)• general case : use log str.M X : can. log str. on X, induced by special fiber(M X = O X ∩ j ∗ O ∗ X K, j : X K ⊂ X)M Y: induced log str. on YL : (N → k, 1 ↦→ 0) a : log str. on Spec k,induced by standard log str. on S, (N → A, 1 → π) a59