Old and new on crystalline cohomology and the de Rham-Witt complex
Abstract
The subject of $p$-adic cohomologies is over fifty years old. Many new developments have recently occurred. I will mostly limit myself to discussing some pertaining to the de Rham-Witt complex. After recalling the historical background and the basic results, I will give an overview of the new approach of Bhatt, Lurie and Mathew.