# Basic Theory of Algebraic *D*-Modules (Fall 2016)

This mini-course was based on the first three chapters of the book *D-Modules, Perverse Sheaves, and Representation Theory* by R. Hotta, K. Takeuchi, and T. Tanisaki. (This book is available free and legally through SpringerLink with a UIC account.) These chapters cover the basic definitions and operations on *D_X*-modules, where *X* is a smooth scheme of pure dimension over an algebraically closed field *k* of characteristic zero.

Our goal was to cover the proofs of **Kashiwara's theorem** and the **Bernstein inequality**. (**Update:** we also covered the proof of preservation of holonomy.)

Notes from the mini-course