Title: "Miscellanea on Crystalline Cohomology"
Abstract: "This talk will cover various ideas that make crystalline
cohomology useful to arithmetic geometers, with a focus on Frobenius.
First, we will carefully sort out the various Frobenius maps and their
actions on cohomology. We will then talk about Mazur's "Newton above Hodge"
theorem and the Cartier isomorphism. After that, we shall explain the uses
in characteristic zero: the p-adic de Rham theorem and crystalline