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

• calculates crystalline cohomology :H ∗ (X, W Ω·X ) = H∗ (X/W )• relates it to :- Serre’s Witt vector cohomology H ∗ (X, W O X )- Artin-Mazur formal gps Φ q associated with H q (−, G m )(Φ 1 = ̂Pic, Φ 2 = ̂Br, etc. )- Hodge cohomology : H j (X, Ω i X ) 4