Vladimir Shein, February 6, 2024
Abstract. I will give an overview of the theory of D-modules in characteristic $p$. In particular, we will discuss a geometric construction of Milne's map from global $1$-forms on a smooth scheme $X$ over a field of characteristic $p$ to the Brauer group of $X$, using the fact that crystalline differential operators are Azumaya over their center, geometrically identified with the Frobenius-twisted cotangent bundle.